If you use machine numbers in the input, then N will not magically make them have higher precision. So the suggestion would be to work with exact numbers. Anything else is just in effect making up digits.

For instance: done with an unlimited decimal places calculator aplying the formula of arc length for the numbers sqrt(1+(0.988639922/0.29719183421)^2) multiplied by the number of digits in the decimal place=69473167820511765242830133883162231196373893172462572947321681009276855429531868770882474054742274999418781196191128350605290638907281085633288937673680524199820066895936872314770237447995716771439959238004273486653770489519884087184561255933086729316005893883052796589968722075656357507968378869005241089165689837538775946470654446499501966076614890157622775988094202464078929288907735084091176712819439586018201262584675330599303231799651328074634544385044419476755076985251636084219268328080088251662043698866454523084731639802544765817015037852583580045461950139773968906062830312323507628556726568436388771648582054725350555439952871014106950029398605002226628662285437033779318551536747294374952255496472680780665826457366896250220249866954099419856397786258180576705276869616498812031948075619511682529816958383878485379938346995226313984712037892411186524390370830098196489452622389323720195586168765517245297601070346396828054779915463530671108671936053175605957994436181065402719501539164 ( non trivial zero)

which is close to :

69473167820511765242830133883162231196373893172462572947321681009276855429531868770882474054742274999418781196191128350605290638907281085633288937673680524199820066895936872314770237447995716771439959238004273486653770489519884087184561255933086729316005893883052796589968722075656357507968378869005241089165689837538775946470654446499501966076614890157622775988094202464078929288907735084091176712819439586018201262584675330599303231799651328074634544385044419476755076985251636084219268328080088251662043698866454523084731639802544765817015037852583580045461950139773968906062830312323507628556726568436388771648582054725350555439952871014106950029398605002226628662285437033779318551536747294374952255496472680780665826457366896250220249866954099419856397786258180576705276869616498812031948075619511682529816958383878485379938346995226313984712037892411186524390370830098196489452622389323720195586168765517245297601070346396828054779915463530671108671936053175605957994436181065402719501539141 ( Prime number ) checked with PrimeQ of wolfram mathematica.

but i can not get this value out of wolfram mathematica!!! Please help P.S: If you are curious to know how i got those numbers please visit " Finding primes and nontivial zeros" at figshare.com under my name Luis Felipe Massena Misiec

I have used DecimalForm and NumberForm, but the results of the calculation keeps me giving the square root of the numbers without giving me the result in numbers it gives me the drawing of the root with the number inside.

n=10000000000000000
a= 0.988639922/0.29719183431
NumberForm[N[a],40]
a1=NumberForm[a]
b=Sqrt[1+a1^2]
N[b]
bb=NumberForm[N[b],40]
b1=DecimalForm[bb]
c=n*b1*2
n=N[c,30]
DecimalForm[c]

`

Have you tried DecimalForm[c]?