Hello Dr. Rohit, as I told you there was a modified version of the program you made so that I found a relation for the x value, it comes about that it varies according to the numbers used in the comparison:
sq=Table[j,{j,100000}]
sq11=Table[j,{j,100,10000}]
n1=Select[sq,OddQ,(2002)]
n=17389
r=0
exp=(((n*x)+n)/n)==((((n*x)+x)/n))-1
eqn=Thread[exp ]
NSolve[#, x] & /@ eqn
sq=Table[j,{j,100000}]
sq11=Table[j,{j,100,10000}]
n2=17393
n1=17389
r=0
exp=(((n2*x)+n2)/n2)==((((n2*x)+x)/n2))-1
eqn=Thread[exp ]
NSolve[#, x] & /@ eqn
exp=((((n2*x)+n2)/n2)-((((n2*x)+x)/n2))/17389)-1==(((n*x)+n)/n)-((((n*x)+x)/n))-1
eqn=Thread[exp ]
NSolve[#, x] & /@ eqn
It gives true to the relation and gives me the value of x that should be considered when equaling the 2 equations, it just so happens that that number is the relation of p/p+1 p is a prime, which then led me to verify that they can be used in predicting the position of prime number without the need of a list, I Made a program to simulate the number interrelated between the 200th -400th prime with the 2000th to the 2200th prime , and I used the prime numbers selected only to have numbers to apply the formula and made a rule of 3 between them and its given position initially known of the first number, so the result of the following program gives the right position for the prime numbers n2 without having to use a list of primes, remember that I only used them to have numbers generated to try out the formula which at least for these conditions give a true result:
sq=Table[j,{j,100000}]
sq11=Table[j,{j,17389,100000}]
sq12=Table[j,{j,1223,100000}]
n1=Select[sq12,PrimeQ,(200)]
n=List[n1]
n2=Select[sq11,PrimeQ,(200)]
a=n1/(n1+1)
b=Select[sq,IntegerQ,(200)]
b1=a*b
c=b1/((n2/(n2+1)))
d=c*10
e=IntegerPart[d]
f=(e/10)+2000
IntegerPart[f]
result:
{2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199} ”
