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Find semi-prime factors; program runs but doesn't compute

Posted 2 years ago

Clear x Clear pnp

    pnp = 85

    f[x] = ((x ^ 3  * pnp^2) / (pnp^2 + x) - x^3)

    For [x = 3, x < pnp/2, (x + 2), Print[x] ; 
     If[ {f[x] > 1}, {x = pnp} ]

different attempt

Clear x
Clear pnp

pnp = 85

f[x] = ((x ^ 3  * pnp^2) / (pnp^2 + x) - x^3)

x = 3; While [f[x] < 1, Print[x]; (x + 2)]
POSTED BY: Bobby Joe Snyder
11 Replies

Attached is a PDF that proves this work.

I hope it is clear enough. I need feedback because I am trying to write an article.

I know it has to be simplified but does anyone follow this?

Attachments:
POSTED BY: Bobby Joe Snyder

Thanks. I was so proud went I imported the 1st 1000 Primes from Wikipedia. I did know about that class library.

But what do you think about the rest.

POSTED BY: Bobby Joe Snyder
p = 3
(p^4/((p*Data)^2 + p) )

N[(Data^4/((p*Data)^2 + Data) )]

Data = Import["C:\\Users\\Trurl\\Documents\\20220405PrimeTable.csv", "CSV"]

These 2 equations are the pattern. N[(Data^4/((pData)^2+Data) )] is the pattern to find the smaller factor and (p^4/((pData)^2+p) ) is the equation to find the pattern of the error. The start is the first 1000 Primes imported from Wikipedia. Notice 2 is not always considered a Prime number and yields imaginary results.

I know I have moved on from this math problem but I thought this post was significant. Looking at the numbers over 1000 instead of 85=5*17.

The RSA formula : N = pq, is factored by N^4/((pN)^2 + N). This is the Pappy Craylar Conjecture. When this equation is less than 1, p is the smaller factor of the semi - Prime N. Which reverses the one - way - function. And is more efficient than recursive division.

Listed below are the examples. Four sets of data. First, the first 1000 Prime numbers are loaded. The error is the test of 3 and the first 1000 Prime factors in set 2 as real number and then set 3 as a decimal. The fourth and final set is the pattern is where 3 is tested and is less than one.

{{"2", 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
   71}, {73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149,
   151, 157, 163, 167, 173}, {179, 181, 191, 193, 197, 199, 211, 223, 227, 
  229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281}, {283, 293, 307, 311,
   313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 
  409}, {419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491,
   499, 503, 509, 521, 523, 541}, {547, 557, 563, 569, 571, 577, 587, 593, 
  599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659}, {661, 673, 677,
   683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 
  797, 809}, {811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883,
   887, 907, 911, 919, 929, 937, 941}, {947, 953, 967, 971, 977, 983, 991, 
  997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 
  1069}, {1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 
  1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223}, {1229, 1231, 1237, 
  1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 
  1321, 1327, 1361, 1367, 1373}, {1381, 1399, 1409, 1423, 1427, 1429, 1433, 
  1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 
  1511}, {1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 
  1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657}, {1663, 1667, 1669, 
  1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 
  1783, 1787, 1789, 1801, 1811}, {1823, 1831, 1847, 1861, 1867, 1871, 1873, 
  1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 
  1987}, {1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 
  2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129}, {2131, 2137, 2141, 
  2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 
  2267, 2269, 2273, 2281, 2287}, {2293, 2297, 2309, 2311, 2333, 2339, 2341, 
  2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 
  2423}, {2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 
  2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617}, {2621, 2633, 2647, 
  2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 
  2713, 2719, 2729, 2731, 2741}, {2749, 2753, 2767, 2777, 2789, 2791, 2797, 
  2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 
  2903}, {2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 
  3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079}, {3083, 3089, 3109, 
  3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 
  3221, 3229, 3251, 3253, 3257}, {3259, 3271, 3299, 3301, 3307, 3313, 3319, 
  3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 
  3413}, {3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 
  3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571}, {3581, 3583, 3593, 
  3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 
  3697, 3701, 3709, 3719, 3727}, {3733, 3739, 3761, 3767, 3769, 3779, 3793, 
  3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 
  3907}, {3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 
  4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057}, {4073, 4079, 4091, 
  4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 
  4211, 4217, 4219, 4229, 4231}, {4241, 4243, 4253, 4259, 4261, 4271, 4273, 
  4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 
  4409}, {4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 
  4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583}, {4591, 4597, 4603, 
  4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 
  4721, 4723, 4729, 4733, 4751}, {4759, 4783, 4787, 4789, 4793, 4799, 4801, 
  4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 
  4937}, {4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 
  5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087}, {5099, 5101, 5107, 
  5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 
  5233, 5237, 5261, 5273, 5279}, {5281, 5297, 5303, 5309, 5323, 5333, 5347, 
  5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 
  5443}, {5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 
  5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639}, {5641, 5647, 5651, 
  5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 
  5743, 5749, 5779, 5783, 5791}, {5801, 5807, 5813, 5821, 5827, 5839, 5843, 
  5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 
  5939}, {5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 
  6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133}, {6143, 6151, 6163, 
  6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 
  6271, 6277, 6287, 6299, 6301}, {6311, 6317, 6323, 6329, 6337, 6343, 6353, 
  6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 
  6473}, {6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 
  6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673}, {6679, 6689, 6691, 
  6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 
  6803, 6823, 6827, 6829, 6833}, {6841, 6857, 6863, 6869, 6871, 6883, 6899, 
  6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 
  6997}, {7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 
  7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207}, {7211, 7213, 7219, 
  7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 
  7349, 7351, 7369, 7393, 7411}, {7417, 7433, 7451, 7457, 7459, 7477, 7481, 
  7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 
  7561}, {7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 
  7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723}, {7727, 7741, 7753, 
  7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 
  7879, 7883, 7901, 7907, 7919}}

p = 3
(p^4/((p*Data)^2 + p) )

3

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  1084, 27/1588, 27/2524, 27/2884, 27/4108, 27/5044, 27/5548, 27/6628, 27/
  8428, 27/10444, 27/11164, 27/13468, 27/15124}, {27/15988, 27/18724, 27/
  20668, 27/23764, 27/28228, 27/30604, 27/31828, 27/34348, 27/35644, 27/38308,
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  66354628, 27/66863524, 27/66920188, 27/67090324, 27/67203868, 27/
  67716004}, {27/67944244, 27/68631268, 27/68746108, 27/68803564, 27/68918548,
   27/69091204, 27/69148804, 27/69494908, 27/69610468, 27/70015684, 27/
  70887964, 27/71179924, 27/71355388, 27/71706964, 27/72118228, 27/72294844, 
  27/72589684, 27/72944284, 27/73003468, 27/73121908}, {27/73299748, 27/
  73537204, 27/73715548, 27/74013268, 27/74072884, 27/74192188, 27/74610508, 
  27/74790148, 27/74970004, 27/75090028, 27/75270244, 27/75330364, 27/
  75631324, 27/75691588, 27/76174564, 27/76537804, 27/76780444, 27/77327788, 
  27/77449684, 27/77632708}, {27/77999404, 27/78060604, 27/78244348, 27/
  78428308, 27/78612484, 27/79474828, 27/79660228, 27/80093668, 27/80217724, 
  27/80466124, 27/80777164, 27/81026428, 27/81401044, 27/81964588, 27/
  82090084, 27/82152868, 27/82278508, 27/83034364, 27/83413588, 27/
  83603524}, {27/83666884, 27/84174628, 27/84365428, 27/84556444, 27/85002988,
   27/85322668, 27/85771228, 27/85899604, 27/86865484, 27/87059308, 27/
  87253348, 27/87447604, 27/87706948, 27/87901708, 27/88031668, 27/88096684, 
  27/88487284, 27/88682908, 27/88813444, 27/88878748}, {27/89074804, 27/
  89795524, 27/89992588, 27/90058324, 27/90189868, 27/90783004, 27/90849028, 
  27/90981148, 27/91378084, 27/91444324, 27/91643188, 27/91775884, 27/
  92640748, 27/92840908, 27/93041284, 27/93174988, 27/93442684, 27/93777844, 
  27/94854388, 27/95394964}, {27/95462644, 27/95665828, 27/95801404, 27/
  95869228, 27/96004948, 27/96072844, 27/96412684, 27/96889468, 27/97094164, 
  27/97230748, 27/97504204, 27/97846564, 27/98052268, 27/98739508, 27/
  98877244, 27/98946148, 27/99153004, 27/100190524, 27/100329268, 27/
  100607044}, {27/100954804, 27/101163748, 27/101372908, 27/101652124, 27/
  101861788, 27/102281764, 27/102421948, 27/102632404, 27/102702604, 27/
  102913348, 27/103053964, 27/103265068, 27/103335484, 27/103687924, 27/
  103758484, 27/104323828, 27/104536228, 27/105245788, 27/105387988, 27/
  105815164}, {27/106314628, 27/107317084, 27/107532508, 27/108252148, 27/
  108396364, 27/109046524, 27/109336108, 27/109553548, 27/109698628, 27/
  109916428, 27/110425468, 27/110643988, 27/110862724, 27/111227764, 27/
  111300844, 27/111666604, 27/112106308, 27/112399924, 27/112767484, 27/
  112841068}, {27/113209348, 27/113504404, 27/113947708, 27/114317788, 27/
  115208428, 27/115282804, 27/115431628, 27/115729564, 27/115953268, 27/
  116102524, 27/116401324, 27/117075028, 27/117450148, 27/117675508, 27/
  117901084, 27/117976324, 27/118202188, 27/118579108, 27/119032204, 27/
  119107804}, {27/119486164, 27/119713468, 27/119940988, 27/120168724, 27/
  120472708, 27/120700948, 27/121081828, 27/121310644, 27/121386964, 27/
  121616068, 27/121845388, 27/122074924, 27/122457964, 27/122764828, 27/
  123687724, 27/123918988, 27/124768804, 27/124846204, 27/125543884, 27/
  125699188}, {27/126010084, 27/126399244, 27/127570324, 27/127883524, 27/
  128589628, 27/128746804, 27/128825428, 27/129218908, 27/129455284, 27/
  129534124, 27/129770788, 27/129928684, 27/130640404, 27/130957348, 27/
  131433484, 27/132149308, 27/132787228, 27/133026844, 27/133106764, 27/
  133586788}, {27/133827124, 27/134228164, 27/134308444, 27/134710204, 27/
  134790628, 27/135032044, 27/135434884, 27/135999868, 27/136161508, 27/
  137133364, 27/137214508, 27/137864524, 27/137945884, 27/138353044, 27/
  138434548, 27/138842428, 27/139659988, 27/139823788, 27/139905724, 27/
  140069668}, {27/140397844, 27/141055348, 27/141302308, 27/141549484, 27/
  141631924, 27/142127068, 27/142788604, 27/143119948, 27/143285764, 27/
  143534668, 27/144782428, 27/144865804, 27/145283044, 27/145366564, 27/
  145617268, 27/145784524, 27/146035588, 27/146286868, 27/146622244, 27/
  146874028}, {27/147042004, 27/147546508, 27/147799084, 27/148136188, 27/
  148642564, 27/148811548, 27/149403748, 27/149912284, 27/150336724, 27/
  151357828, 27/151613644, 27/152125924, 27/152382388, 27/152467924, 27/
  153410404, 27/153753844, 27/154527988, 27/154958908, 27/155217748, 27/
  155822548}, {27/155995564, 27/156082108, 27/156341884, 27/156775324, 27/
  157122508, 27/157383148, 27/157557028, 27/157818028, 27/159126268, 27/
  159738628, 27/160176748, 27/160264444, 27/160791124, 27/161230684, 27/
  161318668, 27/162023404, 27/162111604, 27/162906484, 27/163969348, 27/
  164768764}, {27/165035668, 27/165748468, 27/166552204, 27/166820548, 27/
  166910044, 27/167716588, 27/167896084, 27/168165508, 27/168255364, 27/
  168705004, 27/169065148, 27/169515868, 27/169786588, 27/170057524, 27/
  170419108, 27/170600044, 27/170871628, 27/170962204, 27/171415444, 27/
  171506164}, {27/172050988, 27/172232788, 27/172505668, 27/172778764, 27/
  172869844, 27/173416828, 27/173599348, 27/174238924, 27/175062964, 27/
  175246348, 27/175521604, 27/176440684, 27/176624788, 27/176993284, 27/
  177269908, 27/177454444, 27/177823804, 27/178008628, 27/178656268, 27/
  178934188}, {27/179119588, 27/179769244, 27/180327028, 27/180513148, 27/
  180606244, 27/182005564, 27/182192548, 27/183316468, 27/183597988, 27/
  183879724, 27/184443844, 27/185008828, 27/185669068, 27/185952388, 27/
  186141388, 27/186235924, 27/186425068, 27/187277404, 27/187561948, 27/
  188131684}}



N[(p^4/((p*Data)^2 + p) )]

{{81./(3. + 9. ("2")^2), 0.964286, 0.355263, 0.182432, 0.0741758, 
  0.0531496, 0.031106, 0.0249077, 0.0170025, 0.0106973, 0.009362, 0.00657254, 
  0.00535289, 0.00486662, 0.00407363, 0.00320361, 0.00258522, 0.00241849, 
  0.00200475, 0.00178524}, {0.00168877, 0.001442, 0.00130637, 0.00113617, 
  0.000956497, 0.000882238, 0.00084831, 0.000786072, 0.000757491, 0.000704814,
   0.00055799, 0.000524435, 0.000479506, 0.000465806, 0.000405381, 
  0.000394714, 0.000365121, 0.000338736, 0.000322704, 
  0.000300708}, {0.000280887, 0.000274714, 0.000246702, 0.000241615, 
  0.000231903, 0.000227265, 0.00020215, 0.00018098, 0.000174658, 0.00017162, 
  0.000165778, 0.000157559, 0.000154955, 0.000142854, 0.000136262, 
  0.000130115, 0.000124376, 0.000122547, 0.000117295, 
  0.00011398}, {0.000112375, 0.000104835, 0.0000954914, 0.0000930508, 
  0.0000918655, 0.0000895617, 0.0000821458, 0.0000792467, 0.000074745, 
  0.0000738908, 0.0000722257, 0.0000698317, 0.0000668204, 0.000064688, 
  0.0000626561, 0.0000613542, 0.0000594761, 0.0000571032, 0.0000559697, 
  0.0000538016}, {0.0000512641, 0.0000507782, 0.0000484493, 0.0000480027, 
  0.0000466996, 0.00004586, 0.0000446426, 0.0000430933, 0.0000423487, 
  0.0000419836, 0.0000412675, 0.0000392257, 0.0000379476, 0.0000373318, 
  0.0000361444, 0.0000355718, 0.0000347381, 0.0000331563, 0.0000329032, 
  0.0000307502}, {0.0000300793, 0.0000290089, 0.0000283939, 0.0000277983, 
  0.0000276039, 0.0000270328, 0.0000261196, 0.0000255937, 0.0000250835, 
  0.0000249169, 0.0000244267, 0.0000239509, 0.0000236413, 0.0000234888, 
  0.0000226039, 0.0000219041, 0.0000217681, 0.0000214998, 0.0000211065, 
  0.0000207239}, {0.0000205987, 0.0000198706, 0.0000196365, 0.000019293, 
  0.0000188489, 0.000018315, 0.000017904, 0.0000174094, 0.0000170284, 
  0.0000167508, 0.0000164799, 0.0000163029, 0.0000159574, 0.0000157055, 
  0.0000155408, 0.0000152191, 0.000015062, 0.0000145309, 0.0000141686, 
  0.0000137513}, {0.0000136836, 0.0000133523, 0.0000132875, 0.0000131593, 
  0.0000130958, 0.0000127855, 0.0000123693, 0.0000122541, 0.0000121971, 
  0.0000120843, 0.0000117015, 0.0000115955, 0.0000115431, 0.0000114392, 
  0.0000109403, 0.0000108444, 0.0000106564, 0.0000104282, 0.0000102509, 
  0.000010164}, {0.0000100356, 9.90961*10^-6, 9.62475*10^-6, 9.54561*10^-6, 
  9.42873*10^-6, 9.31398*10^-6, 9.16421*10^-6, 9.05424*10^-6, 8.84016*10^-6, 
  8.77048*10^-6, 8.6675*10^-6, 8.63358*10^-6, 8.46691*10^-6, 8.43416*10^-6, 
  8.33703*10^-6, 8.17883*10^-6, 8.14774*10^-6, 7.99487*10^-6, 7.96482*10^-6, 
  7.87566*10^-6}, {7.61699*10^-6, 7.56124*10^-6, 7.53359*10^-6, 7.47875*10^-6,
   7.39761*10^-6, 7.31778*10^-6, 7.21333*10^-6, 7.13646*10^-6, 7.06081*10^-6, 
  6.79347*10^-6, 6.76992*10^-6, 6.654*10^-6, 6.5634*10^-6, 6.45272*10^-6, 
  6.38765*10^-6, 6.32356*10^-6, 6.23959*10^-6, 6.11675*10^-6, 6.07661*10^-6, 
  6.01713*10^-6}, {5.95852*10^-6, 5.93918*10^-6, 5.8817*10^-6, 5.76923*10^-6, 
  5.67794*10^-6, 5.519*10^-6, 5.50176*10^-6, 5.4675*10^-6, 5.41672*10^-6, 
  5.39995*10^-6, 5.35011*10^-6, 5.31726*10^-6, 5.30095*10^-6, 5.26855*10^-6, 
  5.17312*10^-6, 5.15747*10^-6, 5.11094*10^-6, 4.85877*10^-6, 4.81621*10^-6, 
  4.77421*10^-6}, {4.71906*10^-6, 4.5984*10^-6, 4.53336*10^-6, 4.4446*10^-6, 
  4.41972*10^-6, 4.40735*10^-6, 4.38278*10^-6, 4.34631*10^-6, 4.29839*10^-6, 
  4.27472*10^-6, 4.26296*10^-6, 4.22797*10^-6, 4.15927*10^-6, 4.10329*10^-6, 
  4.09223*10^-6, 4.07024*10^-6, 4.05932*10^-6, 4.0376*10^-6, 4.00534*10^-6, 
  3.94197*10^-6}, {3.8801*10^-6, 3.83965*10^-6, 3.78016*10^-6, 3.75094*10^-6, 
  3.73164*10^-6, 3.70297*10^-6, 3.66526*10^-6, 3.64662*10^-6, 3.60976*10^-6, 
  3.59154*10^-6, 3.52885*10^-6, 3.51123*10^-6, 3.48506*10^-6, 3.4764*10^-6, 
  3.45918*10^-6, 3.43359*10^-6, 3.42512*10^-6, 3.39991*10^-6, 3.3585*10^-6, 
  3.27791*10^-6}, {3.2543*10^-6, 3.2387*10^-6, 3.23095*10^-6, 3.13999*10^-6, 
  3.12521*10^-6, 3.11785*10^-6, 3.08147*10^-6, 3.03865*10^-6, 3.0316*10^-6, 
  2.99671*10^-6, 2.96924*10^-6, 2.94888*10^-6, 2.92873*10^-6, 2.90878*10^-6, 
  2.85015*10^-6, 2.831*10^-6, 2.81834*10^-6, 2.81204*10^-6, 2.77469*10^-6, 
  2.74414*10^-6}, {2.70813*10^-6, 2.68451*10^-6, 2.63821*10^-6, 2.59866*10^-6,
   2.58199*10^-6, 2.57096*10^-6, 2.56547*10^-6, 2.55455*10^-6, 2.54911*10^-6, 
  2.52219*10^-6, 2.49045*10^-6, 2.47481*10^-6, 2.45931*10^-6, 2.41367*10^-6, 
  2.40868*10^-6, 2.36929*10^-6, 2.36444*10^-6, 2.312*10^-6, 2.298*10^-6, 
  2.27954*10^-6}, {2.26583*10^-6, 2.25677*10^-6, 2.25225*10^-6, 2.24326*10^-6,
   2.22545*10^-6, 2.21223*10^-6, 2.19046*10^-6, 2.18614*10^-6, 2.16475*10^-6, 
  2.13533*10^-6, 2.11468*10^-6, 2.10243*10^-6, 2.07825*10^-6, 2.07426*10^-6, 
  2.06632*10^-6, 2.06237*10^-6, 2.04276*10^-6, 2.0196*10^-6, 2.01578*10^-6, 
  1.9856*10^-6}, {1.98187*10^-6, 1.97076*10^-6, 1.9634*10^-6, 1.95974*10^-6, 
  1.94158*10^-6, 1.92723*10^-6, 1.89552*10^-6, 1.85444*10^-6, 1.84773*10^-6, 
  1.83772*10^-6, 1.82451*10^-6, 1.7985*10^-6, 1.79529*10^-6, 1.78889*10^-6, 
  1.7762*10^-6, 1.75121*10^-6, 1.74813*10^-6, 1.74198*10^-6, 1.72978*10^-6, 
  1.72072*10^-6}, {1.71173*10^-6, 1.70577*10^-6, 1.68809*10^-6, 1.68517*10^-6,
   1.65353*10^-6, 1.64506*10^-6, 1.64225*10^-6, 1.63387*10^-6, 1.62831*10^-6, 
  1.62003*10^-6, 1.60096*10^-6, 1.59288*10^-6, 1.58754*10^-6, 1.58487*10^-6, 
  1.57692*10^-6, 1.57165*10^-6, 1.5638*10^-6, 1.54827*10^-6, 1.5406*10^-6, 
  1.53298*10^-6}, {1.51541*10^-6, 1.51045*10^-6, 1.50305*10^-6, 1.48842*10^-6,
   1.47878*10^-6, 1.47162*10^-6, 1.46687*10^-6, 1.43655*10^-6, 1.41611*10^-6, 
  1.40494*10^-6, 1.3961*10^-6, 1.39171*10^-6, 1.38517*10^-6, 1.383*10^-6, 
  1.37652*10^-6, 1.35313*10^-6, 1.34063*10^-6, 1.33856*10^-6, 1.32219*10^-6, 
  1.31412*10^-6}, {1.31011*10^-6, 1.2982*10^-6, 1.2845*10^-6, 1.27485*10^-6, 
  1.27293*10^-6, 1.26911*10^-6, 1.26152*10^-6, 1.25587*10^-6, 1.25026*10^-6, 
  1.24654*10^-6, 1.24469*10^-6, 1.24099*10^-6, 1.23548*10^-6, 1.22819*10^-6, 
  1.22457*10^-6, 1.22276*10^-6, 1.21737*10^-6, 1.20847*10^-6, 1.2067*10^-6, 
  1.19791*10^-6}, {1.19095*10^-6, 1.18749*10^-6, 1.1755*10^-6, 1.16705*10^-6, 
  1.15703*10^-6, 1.15537*10^-6, 1.15042*10^-6, 1.14714*10^-6, 1.1455*10^-6, 
  1.13254*10^-6, 1.12137*10^-6, 1.11821*10^-6, 1.1135*10^-6, 1.10726*10^-6, 
  1.10261*10^-6, 1.09953*10^-6, 1.08582*10^-6, 1.07981*10^-6, 1.07237*10^-6, 
  1.06794*10^-6}, {1.06354*10^-6, 1.05772*10^-6, 1.0505*10^-6, 1.04194*10^-6, 
  1.03209*10^-6, 1.02929*10^-6, 1.02513*10^-6, 1.02099*10^-6, 1.01962*10^-6, 
  1.00067*10^-6, 9.99334*10^-7, 9.92707*10^-7, 9.87453*10^-7, 9.84841*10^-7, 
  9.75782*10^-7, 9.73217*10^-7, 9.68117*10^-7, 9.60541*10^-7, 9.56786*10^-7, 
  9.49343*10^-7}, {9.46881*10^-7, 9.43206*10^-7, 9.3111*10^-7, 9.25149*10^-7, 
  9.23964*10^-7, 9.14563*10^-7, 8.99589*10^-7, 8.97318*10^-7, 8.96186*10^-7, 
  8.89437*10^-7, 8.86091*10^-7, 8.83871*10^-7, 8.77261*10^-7, 8.73983*10^-7, 
  8.69642*10^-7, 8.67483*10^-7, 8.6319*10^-7, 8.51547*10^-7, 8.505*10^-7, 
  8.48412*10^-7}, {8.47371*10^-7, 8.41165*10^-7, 8.26947*10^-7, 8.25946*10^-7,
   8.22951*10^-7, 8.19973*10^-7, 8.17011*10^-7, 8.15045*10^-7, 8.1211*10^-7, 
  8.11135*10^-7, 8.05322*10^-7, 8.03399*10^-7, 7.97669*10^-7, 7.9672*10^-7, 
  7.92*10^-7, 7.91061*10^-7, 7.83609*10^-7, 7.82685*10^-7, 7.75351*10^-7, 
  7.72627*10^-7}, {7.63651*10^-7, 7.56582*10^-7, 7.53085*10^-7, 7.51345*10^-7,
   7.50477*10^-7, 7.48747*10^-7, 7.47883*10^-7, 7.38487*10^-7, 7.35114*10^-7, 
  7.30097*10^-7, 7.27608*10^-7, 7.23488*10^-7, 7.22669*10^-7, 7.21033*10^-7, 
  7.1859*10^-7, 7.17779*10^-7, 7.15353*10^-7, 7.11336*10^-7, 7.10537*10^-7, 
  7.05769*10^-7}, {7.01833*10^-7, 7.0105*10^-7, 6.97153*10^-7, 6.91752*10^-7, 
  6.89456*10^-7, 6.87932*10^-7, 6.85655*10^-7, 6.82637*10^-7, 6.80387*10^-7, 
  6.78147*10^-7, 6.7223*10^-7, 6.67842*10^-7, 6.67115*10^-7, 6.65664*10^-7, 
  6.60624*10^-7, 6.58482*10^-7, 6.57059*10^-7, 6.54228*10^-7, 6.50714*10^-7, 
  6.47923*10^-7}, {6.45842*10^-7, 6.43771*10^-7, 6.36262*10^-7, 6.34237*10^-7,
   6.33564*10^-7, 6.30215*10^-7, 6.25571*10^-7, 6.24254*10^-7, 6.22286*10^-7, 
  6.16437*10^-7, 6.15792*10^-7, 6.12583*10^-7, 6.08132*10^-7, 6.0687*10^-7, 
  6.0624*10^-7, 6.03105*10^-7, 5.98757*10^-7, 5.97524*10^-7, 5.95068*10^-7, 
  5.89598*10^-7}, {5.88392*10^-7, 5.86591*10^-7, 5.85992*10^-7, 5.84798*10^-7,
   5.83013*10^-7, 5.8242*10^-7, 5.78881*10^-7, 5.77708*10^-7, 5.71897*10^-7, 
  5.65607*10^-7, 5.62219*10^-7, 5.61657*10^-7, 5.60536*10^-7, 5.58861*10^-7, 
  5.57194*10^-7, 5.5664*10^-7, 5.54982*10^-7, 5.48968*10^-7, 5.48426*10^-7, 
  5.46805*10^-7}, {5.42517*10^-7, 5.40923*10^-7, 5.37754*10^-7, 5.37228*10^-7,
   5.35657*10^-7, 5.32534*10^-7, 5.28413*10^-7, 5.27901*10^-7, 5.2688*10^-7, 
  5.25354*10^-7, 5.21817*10^-7, 5.20814*10^-7, 5.20313*10^-7, 5.15838*10^-7, 
  5.09961*10^-7, 5.07542*10^-7, 5.06099*10^-7, 5.05619*10^-7, 5.03231*10^-7, 
  5.02755*10^-7}, {5.00387*10^-7, 4.99915*10^-7, 4.97567*10^-7, 4.96166*10^-7,
   4.95701*10^-7, 4.93382*10^-7, 4.9292*10^-7, 4.90621*10^-7, 4.8925*10^-7, 
  4.87429*10^-7, 4.80694*10^-7, 4.7848*10^-7, 4.78039*10^-7, 4.75843*10^-7, 
  4.74097*10^-7, 4.72794*10^-7, 4.70634*10^-7, 4.66784*10^-7, 4.65511*10^-7, 
  4.6298*10^-7}, {4.6047*10^-7, 4.60054*10^-7, 4.56332*10^-7, 4.55101*10^-7, 
  4.54284*10^-7, 4.53062*10^-7, 4.51844*10^-7, 4.48221*10^-7, 4.47822*10^-7, 
  4.4583*10^-7, 4.43065*10^-7, 4.41888*10^-7, 4.41105*10^-7, 4.40715*10^-7, 
  4.39936*10^-7, 4.35304*10^-7, 4.34921*10^-7, 4.32636*10^-7, 4.315*10^-7, 
  4.28492*10^-7}, {4.27*10^-7, 4.25886*10^-7, 4.24777*10^-7, 4.21474*10^-7, 
  4.1857*10^-7, 4.18209*10^-7, 4.17489*10^-7, 4.16412*10^-7, 4.16054*10^-7, 
  4.14983*10^-7, 4.13915*10^-7, 4.12146*10^-7, 4.1109*10^-7, 4.08989*10^-7, 
  4.06905*10^-7, 4.03808*10^-7, 4.03466*10^-7, 4.02443*10^-7, 4.01763*10^-7, 
  3.98724*10^-7}, {3.97385*10^-7, 3.93407*10^-7, 3.9275*10^-7, 3.92422*10^-7, 
  3.91767*10^-7, 3.90788*10^-7, 3.90462*10^-7, 3.88518*10^-7, 3.87873*10^-7, 
  3.85628*10^-7, 3.80883*10^-7, 3.7932*10^-7, 3.78388*10^-7, 3.76532*10^-7, 
  3.74385*10^-7, 3.73471*10^-7, 3.71954*10^-7, 3.70146*10^-7, 3.69845*10^-7, 
  3.69246*10^-7}, {3.68351*10^-7, 3.67161*10^-7, 3.66273*10^-7, 3.64799*10^-7,
   3.64506*10^-7, 3.6392*10^-7, 3.61879*10^-7, 3.6101*10^-7, 3.60144*10^-7, 
  3.59568*10^-7, 3.58707*10^-7, 3.58421*10^-7, 3.56995*10^-7, 3.56711*10^-7, 
  3.54449*10^-7, 3.52767*10^-7, 3.51652*10^-7, 3.49163*10^-7, 3.48613*10^-7, 
  3.47792*10^-7}, {3.46156*10^-7, 3.45885*10^-7, 3.45073*10^-7, 3.44263*10^-7,
   3.43457*10^-7, 3.3973*10^-7, 3.3894*10^-7, 3.37105*10^-7, 3.36584*10^-7, 
  3.35545*10^-7, 3.34253*10^-7, 3.33225*10^-7, 3.31691*10^-7, 3.29411*10^-7, 
  3.28907*10^-7, 3.28656*10^-7, 3.28154*10^-7, 3.25167*10^-7, 3.23688*10^-7, 
  3.22953*10^-7}, {3.22708*10^-7, 3.20762*10^-7, 3.20036*10^-7, 3.19313*10^-7,
   3.17636*10^-7, 3.16446*10^-7, 3.14791*10^-7, 3.1432*10^-7, 3.10825*10^-7, 
  3.10133*10^-7, 3.09444*10^-7, 3.08756*10^-7, 3.07843*10^-7, 3.07161*10^-7, 
  3.06708*10^-7, 3.06481*10^-7, 3.05129*10^-7, 3.04456*10^-7, 3.04008*10^-7, 
  3.03785*10^-7}, {3.03116*10^-7, 3.00683*10^-7, 3.00025*10^-7, 2.99806*10^-7,
   2.99368*10^-7, 2.97412*10^-7, 2.97196*10^-7, 2.96765*10^-7, 2.95476*10^-7, 
  2.95262*10^-7, 2.94621*10^-7, 2.94195*10^-7, 2.91448*10^-7, 2.9082*10^-7, 
  2.90194*10^-7, 2.89777*10^-7, 2.88947*10^-7, 2.87914*10^-7, 2.84647*10^-7, 
  2.83034*10^-7}, {2.82833*10^-7, 2.82232*10^-7, 2.81833*10^-7, 2.81634*10^-7,
   2.81236*10^-7, 2.81037*10^-7, 2.80046*10^-7, 2.78668*10^-7, 2.78081*10^-7, 
  2.7769*10^-7, 2.76911*10^-7, 2.75942*10^-7, 2.75363*10^-7, 2.73447*10^-7, 
  2.73066*10^-7, 2.72876*10^-7, 2.72306*10^-7, 2.69487*10^-7, 2.69114*10^-7, 
  2.68371*10^-7}, {2.67446*10^-7, 2.66894*10^-7, 2.66343*10^-7, 2.65612*10^-7,
   2.65065*10^-7, 2.63977*10^-7, 2.63615*10^-7, 2.63075*10^-7, 2.62895*10^-7, 
  2.62357*10^-7, 2.61999*10^-7, 2.61463*10^-7, 2.61285*10^-7, 2.60397*10^-7, 
  2.6022*10^-7, 2.5881*10^-7, 2.58284*10^-7, 2.56542*10^-7, 2.56196*10^-7, 
  2.55162*10^-7}, {2.53963*10^-7, 2.51591*10^-7, 2.51087*10^-7, 2.49418*10^-7,
   2.49086*10^-7, 2.47601*10^-7, 2.46945*10^-7, 2.46455*10^-7, 2.46129*10^-7, 
  2.45641*10^-7, 2.44509*10^-7, 2.44026*10^-7, 2.43544*10^-7, 2.42745*10^-7, 
  2.42586*10^-7, 2.41791*10^-7, 2.40843*10^-7, 2.40214*10^-7, 2.39431*10^-7, 
  2.39275*10^-7}, {2.38496*10^-7, 2.37876*10^-7, 2.36951*10^-7, 2.36184*10^-7,
   2.34358*10^-7, 2.34207*10^-7, 2.33905*10^-7, 2.33303*10^-7, 2.32852*10^-7, 
  2.32553*10^-7, 2.31956*10^-7, 2.30621*10^-7, 2.29885*10^-7, 2.29445*10^-7, 
  2.29006*10^-7, 2.28859*10^-7, 2.28422*10^-7, 2.27696*10^-7, 2.26829*10^-7, 
  2.26685*10^-7}, {2.25968*10^-7, 2.25539*10^-7, 2.25111*10^-7, 2.24684*10^-7,
   2.24117*10^-7, 2.23693*10^-7, 2.2299*10^-7, 2.22569*10^-7, 2.22429*10^-7, 
  2.2201*10^-7, 2.21592*10^-7, 2.21176*10^-7, 2.20484*10^-7, 2.19933*10^-7, 
  2.18292*10^-7, 2.17884*10^-7, 2.164*10^-7, 2.16266*10^-7, 2.15064*10^-7, 
  2.14799*10^-7}, {2.14269*10^-7, 2.13609*10^-7, 2.11648*10^-7, 2.1113*10^-7, 
  2.0997*10^-7, 2.09714*10^-7, 2.09586*10^-7, 2.08948*10^-7, 2.08566*10^-7, 
  2.08439*10^-7, 2.08059*10^-7, 2.07806*10^-7, 2.06674*10^-7, 2.06174*10^-7, 
  2.05427*10^-7, 2.04314*10^-7, 2.03333*10^-7, 2.02967*10^-7, 2.02845*10^-7, 
  2.02116*10^-7}, {2.01753*10^-7, 2.0115*10^-7, 2.0103*10^-7, 2.0043*10^-7, 
  2.00311*10^-7, 1.99953*10^-7, 1.99358*10^-7, 1.9853*10^-7, 1.98294*10^-7, 
  1.96889*10^-7, 1.96772*10^-7, 1.95844*10^-7, 1.95729*10^-7, 1.95153*10^-7, 
  1.95038*10^-7, 1.94465*10^-7, 1.93327*10^-7, 1.931*10^-7, 1.92987*10^-7, 
  1.92761*10^-7}, {1.92311*10^-7, 1.91414*10^-7, 1.9108*10^-7, 1.90746*10^-7, 
  1.90635*10^-7, 1.89971*10^-7, 1.89091*10^-7, 1.88653*10^-7, 1.88435*10^-7, 
  1.88108*10^-7, 1.86487*10^-7, 1.86379*10^-7, 1.85844*10^-7, 1.85737*10^-7, 
  1.85418*10^-7, 1.85205*10^-7, 1.84886*10^-7, 1.84569*10^-7, 1.84147*10^-7, 
  1.83831*10^-7}, {1.83621*10^-7, 1.82993*10^-7, 1.8268*10^-7, 1.82265*10^-7, 
  1.81644*10^-7, 1.81438*10^-7, 1.80718*10^-7, 1.80105*10^-7, 1.79597*10^-7, 
  1.78385*10^-7, 1.78084*10^-7, 1.77485*10^-7, 1.77186*10^-7, 1.77086*10^-7, 
  1.75998*10^-7, 1.75605*10^-7, 1.74726*10^-7, 1.7424*10^-7, 1.73949*10^-7, 
  1.73274*10^-7}, {1.73082*10^-7, 1.72986*10^-7, 1.72698*10^-7, 1.72221*10^-7,
   1.7184*10^-7, 1.71556*10^-7, 1.71367*10^-7, 1.71083*10^-7, 1.69677*10^-7, 
  1.69026*10^-7, 1.68564*10^-7, 1.68472*10^-7, 1.6792*10^-7, 1.67462*10^-7, 
  1.67371*10^-7, 1.66643*10^-7, 1.66552*10^-7, 1.65739*10^-7, 1.64665*10^-7, 
  1.63866*10^-7}, {1.63601*10^-7, 1.62897*10^-7, 1.62111*10^-7, 1.61851*10^-7,
   1.61764*10^-7, 1.60986*10^-7, 1.60814*10^-7, 1.60556*10^-7, 1.6047*10^-7, 
  1.60043*10^-7, 1.59702*10^-7, 1.59277*10^-7, 1.59023*10^-7, 1.5877*10^-7, 
  1.58433*10^-7, 1.58265*10^-7, 1.58013*10^-7, 1.5793*10^-7, 1.57512*10^-7, 
  1.57429*10^-7}, {1.5693*10^-7, 1.56765*10^-7, 1.56517*10^-7, 1.56269*10^-7, 
  1.56187*10^-7, 1.55694*10^-7, 1.55531*10^-7, 1.5496*10^-7, 1.5423*10^-7, 
  1.54069*10^-7, 1.53827*10^-7, 1.53026*10^-7, 1.52866*10^-7, 1.52548*10^-7, 
  1.5231*10^-7, 1.52152*10^-7, 1.51836*10^-7, 1.51678*10^-7, 1.51128*10^-7, 
  1.50893*10^-7}, {1.50737*10^-7, 1.50193*10^-7, 1.49728*10^-7, 1.49574*10^-7,
   1.49496*10^-7, 1.48347*10^-7, 1.48195*10^-7, 1.47286*10^-7, 1.4706*10^-7, 
  1.46835*10^-7, 1.46386*10^-7, 1.45939*10^-7, 1.4542*10^-7, 1.45198*10^-7, 
  1.45051*10^-7, 1.44977*10^-7, 1.4483*10^-7, 1.44171*10^-7, 1.43952*10^-7, 
  1.43516*10^-7}}










N[(Data^4/((p*Data)^2 + Data) )]

{{("2")^4/("2" + 9. ("2")^2), 0.964286, 2.71739, 5.35938, 13.31, 
  18.6186, 31.9026, 39.8779, 58.4952, 93.0878, 106.396, 151.656, 186.273, 
  204.915, 244.866, 311.458, 386.051, 412.693, 497.952, 559.236}, {591.211, 
  692.471, 764.421, 879.014, 1044.25, 1132.2, 1177.51, 1270.79, 1318.77, 
  1417.38, 1790.54, 1905.16, 2083.75, 2145.06, 2464.94, 2531.58, 2736.84, 
  2950.1, 3096.72, 3323.31}, {3557.9, 3637.88, 4051.09, 4136.4, 4309.68, 
  4397.66, 4944.17, 5522.69, 5722.64, 5823.95, 6029.24, 6343.83, 6450.47, 
  6997.01, 7335.61, 7682.2, 8036.79, 8156.77, 8522.03, 8769.98}, {8895.29, 
  9535.16, 10468.3, 10742.9, 10881.6, 11161.5, 12169.4, 12614.6, 13374.5, 
  13529.1, 13841.1, 14315.7, 14960.9, 15454.2, 15955.4, 16294.1, 16808.6, 
  17507.2, 17861.8, 18581.7}, {19501.6, 19688.2, 20634.8, 20826.8, 21408., 
  21800., 22394.6, 23199.8, 23607.8, 23813.1, 24226.3, 25487.5, 26346.1, 
  26780.7, 27660.6, 28105.9, 28780.5, 30153.7, 30385.7, 32513.4}, {33238.7, 
  34465.2, 35211.8, 35966.4, 36219.7, 36985., 38278.2, 39064.8, 39859.4, 
  40126., 40931.3, 41744.5, 42291.2, 42565.8, 44232.3, 45645.5, 45930.8, 
  46504.1, 47370.7, 48245.3}, {48538.6, 50317.1, 50917.1, 51823.7, 53044.9, 
  54591.5, 55844.7, 57431.2, 58716.5, 59689.7, 60671., 61329.6, 62657.5, 
  63662.8, 64337.4, 65697.3, 66382.6, 68809.1, 70568.9, 72710.1}, {73070.1, 
  74883.3, 75248.6, 75981.9, 76349.9, 78203.1, 80834.9, 81594.9, 81976.2, 
  82741.5, 85448., 86229.2, 86621.2, 87407.8, 91394.2, 92202.2, 93828.8, 
  95882., 97540.5, 98375.2}, {99633.8, 100900., 103887., 104748., 106047., 
  107353., 109108., 110433., 113108., 114006., 115361., 115814., 118094., 
  118553., 119934., 122254., 122720., 125067., 125539., 126960.}, {131272., 
  132240., 132725., 133699., 135165., 136640., 138618., 140112., 141613., 
  147186., 147698., 150271., 152346., 154959., 156537., 158124., 160252., 
  163470., 164550., 166177.}, {167812., 168358., 170004., 173318., 176105., 
  181176., 181744., 182883., 184598., 185171., 186896., 188051., 188629., 
  189789., 193290., 193877., 195642., 205797., 207615., 209442.}, {211890., 
  217450., 220569., 224975., 226241., 226876., 228148., 230062., 232628., 
  233916., 234561., 236502., 240409., 243688., 244347., 245667., 246328., 
  247654., 249648., 253661.}, {257707., 260421., 264520., 266581., 267960., 
  270034., 272813., 274207., 277007., 278413., 283359., 284780., 286919., 
  287634., 289066., 291220., 291940., 294105., 297732., 305052.}, {307265., 
  308745., 309486., 318451., 319958., 320712., 324499., 329072., 329838., 
  333677., 336765., 339091., 341424., 343765., 350837., 353210., 354797., 
  355591., 360378., 364391.}, {369236., 372484., 379023., 384790., 387276., 
  388937., 389769., 391436., 392270., 396457., 401510., 404049., 406595., 
  414283., 415142., 422043., 422909., 432501., 435136., 438661.}, {441314., 
  443087., 443975., 445754., 449322., 452007., 456500., 457402., 461922., 
  468287., 472860., 475615., 481148., 482073., 483926., 484854., 489508., 
  495121., 496059., 503600.}, {504547., 507392., 509294., 510246., 515019., 
  518853., 527533., 539218., 541178., 544125., 548066., 555991., 556986., 
  558978., 562972., 571004., 572012., 574031., 578079., 581124.}, {584177., 
  586217., 592358., 593385., 604737., 607851., 608891., 612016., 614104., 
  617243., 624598., 627763., 629877., 630936., 634117., 636243., 639437., 
  645850., 649069., 652296.}, {659855., 662023., 665282., 671823., 676202., 
  679495., 681695., 696081., 706129., 711742., 716249., 718507., 721902., 
  723035., 726441., 738995., 745888., 747040., 756288., 760933.}, {763261., 
  770266., 778479., 784373., 785554., 787919., 792660., 796226., 799799., 
  802186., 803380., 805772., 809367., 814172., 816580., 817785., 821407., 
  827460., 828673., 834753.}, {839633., 842078., 850665., 856824., 864246., 
  865486., 869211., 871699., 872944., 882939., 891730., 894250., 898037., 
  903098., 906904., 909445., 920925., 926050., 932476., 936343.}, {940218., 
  945396., 951889., 959710., 968876., 971502., 975449., 979403., 980723., 
  999296., 1.00063*10^6, 1.00731*10^6, 1.01267*10^6, 1.01535*10^6, 
  1.02478*10^6, 1.02748*10^6, 1.0329*10^6, 1.04104*10^6, 1.04513*10^6, 
  1.05332*10^6}, {1.05606*10^6, 1.06018*10^6, 1.07395*10^6, 1.08087*10^6, 
  1.08225*10^6, 1.09338*10^6, 1.11158*10^6, 1.11439*10^6, 1.1158*10^6, 
  1.12427*10^6, 1.12851*10^6, 1.13135*10^6, 1.13987*10^6, 1.14415*10^6, 
  1.14986*10^6, 1.15272*10^6, 1.15845*10^6, 1.17429*10^6, 1.17574*10^6, 
  1.17863*10^6}, {1.18008*10^6, 1.18879*10^6, 1.20923*10^6, 1.21069*10^6, 
  1.2151*10^6, 1.21951*10^6, 1.22393*10^6, 1.22688*10^6, 1.23132*10^6, 
  1.2328*10^6, 1.2417*10^6, 1.24467*10^6, 1.25361*10^6, 1.25511*10^6, 
  1.26259*10^6, 1.26408*10^6, 1.2761*10^6, 1.27761*10^6, 1.2897*10^6, 
  1.29424*10^6}, {1.30946*10^6, 1.32169*10^6, 1.32783*10^6, 1.3309*10^6, 
  1.33244*10^6, 1.33552*10^6, 1.33706*10^6, 1.35408*10^6, 1.36029*10^6, 
  1.36964*10^6, 1.37432*10^6, 1.38215*10^6, 1.38372*10^6, 1.38686*10^6, 
  1.39157*10^6, 1.39314*10^6, 1.39787*10^6, 1.40576*10^6, 1.40734*10^6, 
  1.41685*10^6}, {1.4248*10^6, 1.42639*10^6, 1.43436*10^6, 1.44556*10^6, 
  1.45037*10^6, 1.45359*10^6, 1.45841*10^6, 1.46486*10^6, 1.46971*10^6, 
  1.47456*10^6, 1.48754*10^6, 1.49731*10^6, 1.49895*10^6, 1.50221*10^6, 
  1.51367*10^6, 1.5186*10^6, 1.52189*10^6, 1.52847*10^6, 1.53673*10^6, 
  1.54335*10^6}, {1.54832*10^6, 1.5533*10^6, 1.57163*10^6, 1.57665*10^6, 
  1.57833*10^6, 1.58671*10^6, 1.59849*10^6, 1.60187*10^6, 1.60693*10^6, 
  1.62218*10^6, 1.62388*10^6, 1.63238*10^6, 1.64433*10^6, 1.64775*10^6, 
  1.64946*10^6, 1.65804*10^6, 1.67008*10^6, 1.67353*10^6, 1.68043*10^6, 
  1.69602*10^6}, {1.6995*10^6, 1.70472*10^6, 1.70646*10^6, 1.70994*10^6, 
  1.71518*10^6, 1.71692*10^6, 1.72742*10^6, 1.73093*10^6, 1.74852*10^6, 
  1.76796*10^6, 1.77862*10^6, 1.7804*10^6, 1.78396*10^6, 1.7893*10^6, 
  1.79466*10^6, 1.79644*10^6, 1.80181*10^6, 1.82155*10^6, 1.82335*10^6, 
  1.82876*10^6}, {1.84321*10^6, 1.84864*10^6, 1.85954*10^6, 1.86135*10^6, 
  1.86682*10^6, 1.87776*10^6, 1.89241*10^6, 1.89424*10^6, 1.89791*10^6, 
  1.90343*10^6, 1.91633*10^6, 1.92002*10^6, 1.92187*10^6, 1.93854*10^6, 
  1.96088*10^6, 1.97023*10^6, 1.97585*10^6, 1.97772*10^6, 1.98711*10^6, 
  1.98899*10^6}, {1.9984*10^6, 2.00029*10^6, 2.00973*10^6, 2.0154*10^6, 
  2.01729*10^6, 2.02677*10^6, 2.02867*10^6, 2.03818*10^6, 2.04389*10^6, 
  2.05153*10^6, 2.08027*10^6, 2.0899*10^6, 2.09183*10^6, 2.10148*10^6, 
  2.10922*10^6, 2.11503*10^6, 2.12474*10^6, 2.14227*10^6, 2.14812*10^6, 
  2.15987*10^6}, {2.17164*10^6, 2.1736*10^6, 2.19133*10^6, 2.19726*10^6, 
  2.20121*10^6, 2.20715*10^6, 2.2131*10^6, 2.23098*10^6, 2.23298*10^6, 
  2.24295*10^6, 2.25695*10^6, 2.26296*10^6, 2.26698*10^6, 2.26898*10^6, 
  2.273*10^6, 2.29719*10^6, 2.29921*10^6, 2.31136*10^6, 2.31744*10^6, 
  2.33371*10^6}, {2.34186*10^6, 2.34799*10^6, 2.35412*10^6, 2.37257*10^6, 
  2.38903*10^6, 2.39109*10^6, 2.39521*10^6, 2.40141*10^6, 2.40348*10^6, 
  2.40968*10^6, 2.41589*10^6, 2.42627*10^6, 2.4325*10^6, 2.445*10^6, 
  2.45752*10^6, 2.47637*10^6, 2.47847*10^6, 2.48477*10^6, 2.48897*10^6, 
  2.50794*10^6}, {2.51639*10^6, 2.54184*10^6, 2.54609*10^6, 2.54822*10^6, 
  2.55248*10^6, 2.55887*10^6, 2.56101*10^6, 2.57383*10^6, 2.57811*10^6, 
  2.59311*10^6, 2.62542*10^6, 2.63623*10^6, 2.64273*10^6, 2.65575*10^6, 
  2.67098*10^6, 2.67753*10^6, 2.68845*10^6, 2.70158*10^6, 2.70377*10^6, 
  2.70816*10^6}, {2.71474*10^6, 2.72354*10^6, 2.73014*10^6, 2.74117*10^6, 
  2.74338*10^6, 2.7478*10^6, 2.76329*10^6, 2.76994*10^6, 2.77661*10^6, 
  2.78105*10^6, 2.78772*10^6, 2.78995*10^6, 2.8011*10^6, 2.80333*10^6, 
  2.82122*10^6, 2.83467*10^6, 2.84366*10^6, 2.86393*10^6, 2.86844*10^6, 
  2.87522*10^6}, {2.8888*10^6, 2.89107*10^6, 2.89788*10^6, 2.90469*10^6, 
  2.91151*10^6, 2.94345*10^6, 2.95032*10^6, 2.96637*10^6, 2.97096*10^6, 
  2.98016*10^6, 2.99168*10^6, 3.00091*10^6, 3.01479*10^6, 3.03566*10^6, 
  3.04031*10^6, 3.04263*10^6, 3.04729*10^6, 3.07528*10^6, 3.08933*10^6, 
  3.09636*10^6}, {3.09871*10^6, 3.11751*10^6, 3.12458*10^6, 3.13165*10^6, 
  3.14819*10^6, 3.16003*10^6, 3.17665*10^6, 3.1814*10^6, 3.21717*10^6, 
  3.22435*10^6, 3.23154*10^6, 3.23873*10^6, 3.24834*10^6, 3.25555*10^6, 
  3.26037*10^6, 3.26277*10^6, 3.27724*10^6, 3.28448*10^6, 3.28932*10^6, 
  3.29174*10^6}, {3.299*10^6, 3.32569*10^6, 3.33299*10^6, 3.33543*10^6, 
  3.3403*10^6, 3.36227*10^6, 3.36471*10^6, 3.3696*10^6, 3.38431*10^6, 
  3.38676*10^6, 3.39412*10^6, 3.39904*10^6, 3.43107*10^6, 3.43848*10^6, 
  3.4459*10^6, 3.45086*10^6, 3.46077*10^6, 3.47318*10^6, 3.51306*10^6, 
  3.53308*10^6}, {3.53558*10^6, 3.54311*10^6, 3.54813*10^6, 3.55064*10^6, 
  3.55567*10^6, 3.55818*10^6, 3.57077*10^6, 3.58843*10^6, 3.59601*10^6, 
  3.60107*10^6, 3.6112*10^6, 3.62388*10^6, 3.63149*10^6, 3.65695*10^6, 
  3.66205*10^6, 3.6646*10^6, 3.67226*10^6, 3.71069*10^6, 3.71583*10^6, 
  3.72612*10^6}, {3.739*10^6, 3.74673*10^6, 3.75448*10^6, 3.76482*10^6, 
  3.77259*10^6, 3.78814*10^6, 3.79333*10^6, 3.80113*10^6, 3.80373*10^6, 
  3.81153*10^6, 3.81674*10^6, 3.82456*10^6, 3.82717*10^6, 3.84022*10^6, 
  3.84283*10^6, 3.86377*10^6, 3.87164*10^6, 3.89792*10^6, 3.90319*10^6, 
  3.91901*10^6}, {3.93751*10^6, 3.97463*10^6, 3.98261*10^6, 4.00926*10^6, 
  4.01461*10^6, 4.03869*10^6, 4.04941*10^6, 4.05746*10^6, 4.06284*10^6, 
  4.0709*10^6, 4.08976*10^6, 4.09785*10^6, 4.10595*10^6, 4.11947*10^6, 
  4.12218*10^6, 4.13572*10^6, 4.15201*10^6, 4.16288*10^6, 4.1765*10^6, 
  4.17922*10^6}, {4.19286*10^6, 4.20379*10^6, 4.22021*10^6, 4.23392*10^6, 
  4.2669*10^6, 4.26966*10^6, 4.27517*10^6, 4.2862*10^6, 4.29449*10^6, 
  4.30002*10^6, 4.31108*10^6, 4.33603*10^6, 4.34993*10^6, 4.35827*10^6, 
  4.36663*10^6, 4.36942*10^6, 4.37778*10^6, 4.39174*10^6, 4.40852*10^6, 
  4.41132*10^6}, {4.42534*10^6, 4.43375*10^6, 4.44218*10^6, 4.45062*10^6, 
  4.46187*10^6, 4.47033*10^6, 4.48443*10^6, 4.49291*10^6, 4.49573*10^6, 
  4.50422*10^6, 4.51271*10^6, 4.52121*10^6, 4.5354*10^6, 4.54677*10^6, 
  4.58095*10^6, 4.58951*10^6, 4.62099*10^6, 4.62385*10^6, 4.64969*10^6, 
  4.65545*10^6}, {4.66696*10^6, 4.68137*10^6, 4.72475*10^6, 4.73635*10^6, 
  4.7625*10^6, 4.76832*10^6, 4.77123*10^6, 4.7858*10^6, 4.79456*10^6, 
  4.79748*10^6, 4.80624*10^6, 4.81209*10^6, 4.83845*10^6, 4.85019*10^6, 
  4.86783*10^6, 4.89434*10^6, 4.91796*10^6, 4.92684*10^6, 4.9298*10^6, 
  4.94758*10^6}, {4.95648*10^6, 4.97133*10^6, 4.9743*10^6, 4.98918*10^6, 
  4.99216*10^6, 5.0011*10^6, 5.01602*10^6, 5.03695*10^6, 5.04294*10^6, 
  5.07893*10^6, 5.08194*10^6, 5.10601*10^6, 5.10902*10^6, 5.1241*10^6, 
  5.12712*10^6, 5.14223*10^6, 5.17251*10^6, 5.17857*10^6, 5.18161*10^6, 
  5.18768*10^6}, {5.19984*10^6, 5.22419*10^6, 5.23333*10^6, 5.24249*10^6, 
  5.24554*10^6, 5.26388*10^6, 5.28838*10^6, 5.30065*10^6, 5.30679*10^6, 
  5.31601*10^6, 5.36223*10^6, 5.36531*10^6, 5.38077*10^6, 5.38386*10^6, 
  5.39315*10^6, 5.39934*10^6, 5.40864*10^6, 5.41795*10^6, 5.43037*10^6, 
  5.43969*10^6}, {5.44591*10^6, 5.4646*10^6, 5.47395*10^6, 5.48644*10^6, 
  5.50519*10^6, 5.51145*10^6, 5.53338*10^6, 5.55222*10^6, 5.56794*10^6, 
  5.60576*10^6, 5.61523*10^6, 5.63421*10^6, 5.6437*10^6, 5.64687*10^6, 
  5.68178*10^6, 5.6945*10^6, 5.72317*10^6, 5.73913*10^6, 5.74872*10^6, 
  5.77112*10^6}, {5.77752*10^6, 5.78073*10^6, 5.79035*10^6, 5.8064*10^6, 
  5.81926*10^6, 5.82892*10^6, 5.83536*10^6, 5.84502*10^6, 5.89348*10^6, 
  5.91616*10^6, 5.93238*10^6, 5.93563*10^6, 5.95514*10^6, 5.97142*10^6, 
  5.97467*10^6, 6.00078*10^6, 6.00404*10^6, 6.03348*10^6, 6.07285*10^6, 
  6.10246*10^6}, {6.11234*10^6, 6.13874*10^6, 6.16851*10^6, 6.17845*10^6, 
  6.18176*10^6, 6.21163*10^6, 6.21828*10^6, 6.22826*10^6, 6.23159*10^6, 
  6.24824*10^6, 6.26158*10^6, 6.27827*10^6, 6.2883*10^6, 6.29833*10^6, 
  6.31173*10^6, 6.31843*10^6, 6.32849*10^6, 6.33184*10^6, 6.34863*10^6, 
  6.35199*10^6}, {6.37217*10^6, 6.3789*10^6, 6.38901*10^6, 6.39912*10^6, 
  6.40249*10^6, 6.42275*10^6, 6.42951*10^6, 6.4532*10^6, 6.48372*10^6, 
  6.49051*10^6, 6.50071*10^6, 6.53475*10^6, 6.54156*10^6, 6.55521*10^6, 
  6.56546*10^6, 6.57229*10^6, 6.58597*10^6, 6.59282*10^6, 6.6168*10^6, 
  6.6271*10^6}, {6.63396*10^6, 6.65802*10^6, 6.67868*10^6, 6.68558*10^6, 
  6.68902*10^6, 6.74085*10^6, 6.74778*10^6, 6.7894*10^6, 6.79983*10^6, 
  6.81026*10^6, 6.83116*10^6, 6.85208*10^6, 6.87653*10^6, 6.88703*10^6, 
  6.89403*10^6, 6.89753*10^6, 6.90453*10^6, 6.9361*10^6, 6.94664*10^6, 
  6.96774*10^6}}
Attachments:
POSTED BY: Bobby Joe Snyder
Posted 2 years ago

First 1000 primes

Array[Prime, 1000]
POSTED BY: Rohit Namjoshi
Posted 2 years ago

Try

Clear[x,pnp,f];
pnp=85;
f[x_]:=x^4/(pnp^2+x);
For[x=3,x<pnp/2,x=x+2,
  If[f[x]<1,Print[x]]
]
POSTED BY: Bill Nelson
Posted 2 years ago

There is a missing ; and a ; that should be a , in the body of the For.

POSTED BY: Rohit Namjoshi

I hope this shows what I was trying to do. Syntax is not correct, I think. It just gives a recursive error.

Clear [x, pnp, f];

pnp = 85



For [x = 3, (x < (pnp/2)), (x = x + 2) ; 
 f[x] = x^4/(pnp^2 + x)
   If[f[x] < 1,
    Print[x]]
 ]

85

$RecursionLimit::reclim2: Recursion depth of 1024 exceeded during evaluation of If[f[5]<1,Print[x]].

$RecursionLimit::reclim2: Recursion depth of 1024 exceeded during evaluation of If[f[7]<1,Print[x]].

$RecursionLimit::reclim2: Recursion depth of 1024 exceeded during evaluation of If[f[9]<1,Print[x]].

General::stop: Further output of $RecursionLimit::reclim2 will be suppressed during this calculation.
POSTED BY: Bobby Joe Snyder

Clear [x, pnp, f];

pnp = 85
x = 3
f[x] = (x^3 - (x ^ 3  * pnp^2) / (pnp^2 + x))



Prime Factors fall where f[x] <1. Loop for x and check equation is less than one. Equation still doesn't run.
Here for a Semi-Prime of 5 the options are 3, 5, or 7 for the smallest Prime factor. 





Out[119]= 85

Out[120]= 3

Out[121]= 81/7228

In[122]:= N[81/7228]

Out[122]= 0.0112064



Out[115]= 85

Out[116]= 11

Out[117]= 14641/7236

In[123]:= N[14641/7236]

Out[123]= 2.02336





Out[111]= 85

Out[112]= 7

Out[113]= 2401/7232

In[124]:= N[2401/7232]

Out[124]= 0.331997



Out[107]= 85

Out[108]= 5

Out[109]= 125/1446

In[125]:= N[125/1446]

Out[125]= 0.0864454
POSTED BY: Bobby Joe Snyder

Yes the equation is always negative. But I only want x values greater than -1.

The SemiPrime smallest factor occurs near zero. I wanted to print the x values near zero.

And break at x values less than -1. It greatly eliminates the possible factors.

You have probably know this and are crunching numbers as I speak. I only ask you share the proper syntax of the program.

And thanks for all the programming help this far.

POSTED BY: Bobby Joe Snyder
Posted 2 years ago

There are several syntax errors.

Clear[x, pnp, f];

f[x_] := ((x^3*pnp^2)/(pnp^2 + x) - x^3)

I don't understand how f is going to compute semi-primes, its value is always negative so the loops never terminate.

Clear[pnp];
((x^3*pnp^2)/(pnp^2 + x) - x^3) // Simplify
(* -(x^4/(pnp^2 + x)) *)

Using built-in WL functions

Range[100] // AssociationMap[FactorInteger] // 
  Select[Total[#[[All, 2]]] == 2 &] // Keys
(* {4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51,
55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95} *)
POSTED BY: Updating Name

You are not resetting x. In particular, x+2 is not the same as x=x+2.

Also the use of Clear is not syntactically correct (it requires brackets e.g. Clear[x]).

POSTED BY: Daniel Lichtblau
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