100 digit base ten primes

• To: mathgroup at smc.vnet.net
• Subject: [mg52252] 100 digit base ten primes
• From: Roger Bagula <tftn at earthlink.net>
• Date: Wed, 17 Nov 2004 02:20:24 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Clear[a,b,m,m0,m1,m3]
(* program for finding primes near 100 digits long base 10 using Mersenne
seed points*)
(* cryptography length primes*)
(* the logically most probable way someone taught*)
(* traditional number theory might use find 100 digits primes*)
(* short of using a sieve to 100 decimal places*)
Table[N[Log[2^Prime[n]]/Log[10]],{n,1,68}]
\$MaxPrecision=Floor[Log[2^Prime[68]]/Log[10]]+1
m=2^Prime[67]-1
m0=Floor[m+Log[m]^2]
(m0-m)/2
m1=2^Prime[68]-1
m3=Floor[m1+Log[m1]^2]
(m3-m1)/2
a=Delete[Union[Table[If[PrimeQ[n]==True,n,0],{n,m,m0,2}]],1]
Dimensions[a][[1]]
(* 1/Log[n] probability test*)
N[Dimensions[a][[1]]/((m0-m)/2)-1/Log[m0]]
b=Delete[Union[Table[If[PrimeQ[n]==True,n,0],{n,m1,m3,2}]],1]
Dimensions[b][[1]]
N[Dimensions[b][[1]]/((m3-m1)/2)-1/Log[m3]]
PrimeQ[m+Floor[Log[m]^2/2]]==True
PrimeQ[m1+Floor[Log[m1]^2/2]]==True

Respectfully, Roger L. Bagula