## Proof of Primes of the form 10^(2k+1)+3

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• 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
Message 1 of 4 , Jul 22, 2005
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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.
Message 2 of 4 , Aug 2, 2005
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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://www.mersenneforum.org/showpost.php?p=52303&postcount=105 Stand alone executables.
Message 3 of 4 , Aug 2, 2005
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> 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. ... __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection
Message 4 of 4 , Aug 2, 2005
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Thanks! Both of you!

Bouk.

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

>
> > I need a p4 version of the latest ECM which will run on XP.
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> http://www.mersenneforum.org/showpost.php?p=52303&postcount=105
>
> Stand alone executables.
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> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
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