- Here is a proof that 10^5+3 is prime and

10^3+3 is not prime using the fact that

10^(2k+1) + 3 is divisible by a prime P

if and only if (P-10)^(2k+1) mod P is 3,

sqrt(10^3+3) = 31.6

sqrt(10^5+3) = 316.2

The numbers (P-10)^5 mod P are given

below for the primes

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,

179,181,191,193,197,199,211,223,227,281,

283,293,307,311,313

0,1,0,5,19,11,16,4,21,

6,11,40,18,16,11,5,40,31,39,

10,14,15,36,7,91,13,45,62,5

25,121,40,122,23,36,72,86,163,107,

16,123,30,189,34,57,41,183,97,159,

219,136,119,211,69,221,21,242,187,273,

164,59,25,305,160

Which proves that 10^5+3 is prime since

no 3 appears in this list.

For 10^3+3 the numbers are:

2,3,5,7,11,13,17,19,23,29,31:

0,1,0,6,1,1,3,7,12,15,23

which shows that 10^3+3 is divisble by 17.

Tables of these numbers can be maintained for each

prime, then divisibility is a matter of table

look-up. And so, is better than division.

This can also be done for 10^(2k+1) + 7 or + 9.

Milton L. Brown - Hello everybody!

This may seem a stupid question but I'm simply not good at making executables

:-)

I need a p4 version of the latest ECM which will run on XP. I'm currently using

the old 5.1 for p4 and it keeps crashing all the time on both my machines.

And could somebody please advise me if I need cygwin or msys to make it run

properly?

Help would be very welcome!

Bouk (who normally let's David almost do all the ECM stuff)

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http://mail.yahoo.com > I need a p4 version of the latest ECM which will run on XP.

http://www.mersenneforum.org/showpost.php?p=52303&postcount=105

Stand alone executables.- Thanks! Both of you!

Bouk.

--- elevensmooth <elevensmooth@...> wrote:

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