2p+1 - Page 2

S80780 · 2003-06-09, 07:08

To your first question: Prime95 is specialised on Mersenne Numbers 2^p-1. To test numbers of a different form, there are other programs like PFGW.

To your second question: As Cheesehead posted, each such prime must be a Fermat Prime 2^(2^n) + 1.

To your third question: Yes. This is so, because 6 * 6 = 36 = 6 (mod 10) and the residue of a product or sum won't change if you reduce the factors / summands to their residues before multiplying / adding them.

Benjamin

2003-06-09, 09:58

Please dont recommend PFGW, to a novice user.
Besides it is much slower than LLR, please see
http://groups.yahoo.com/group/openpfgw/message/374

LLR is a generalized mersenne test for primes of the form (k*2^n-1)

Come join us at the 15k search forum here. ;)

clowns789 · 2003-06-09, 15:52

So I guess you might as well do the old 2^p-1 so it would go the fastest.

I was thinking with the 2^p+1 and 16^p+1 you can find all three types of primes (regular, Mersenne, and Fermat) that you wouldn't with 2^p-1.

S80780 · 2003-06-09, 20:16

Quote:

Originally Posted by TTn

Please dont recommend PFGW, to a novice user.
Besides it is much slower than LLR, please see
http://groups.yahoo.com/group/openpfgw/message/374

LLR is a generalized mersenne test for primes of the form (k*2^n-1)

Thanks for this hint. As a GIMPSter, I usually think of LLR as - Residue instead of - Riesel.:D

Quote:

Originally Posted by clowns789

So I guess you might as well do the old 2^p-1 so it would go the fastest.

I was thinking with the 2^p+1 and 16^p+1 you can find all three types of primes (regular, Mersenne, and Fermat) that you wouldn't with 2^p-1.

No. Mersenne - (2^n - 1), Fermat - (2^(2^n) + 1), Proth - (k^n - 1), generalized Mersenne - Numbers (k*2^n - 1) etc. are just names for numbers of a special form.
For some of them, like the Mersenne - Numbers, special algorithms are known to determine their primality. Others can only be tested with general primality tests.

By the way, if you set a = 2^(2^k), b = 1 in the formula, I stated, you can see that every even power of two plus 1 is devisable at least by a Fermat - Number. So sorry for making such a fuss about nothing.

Benjamin

smh · 2003-06-10, 10:11

Quote:

Please dont recommend PFGW, to a novice user.
Besides it is much slower than LLR, please see

Can LLR test numbers of the form 2^p+1 (ie K=1)?

LLR is faster then PRP and PFWG for numbers of the form k*2^P-1, but a while ago i did some tests on numbers of the form K*2^P+1 and all 3 had about the same speed (with the latest PFGW slightly faster then the others)

2003-06-09, 07:08	#12
S80780 Jan 2003 far from M40 5³ Posts	To your first question: Prime95 is specialised on Mersenne Numbers 2^p-1. To test numbers of a different form, there are other programs like PFGW. To your second question: As Cheesehead posted, each such prime must be a Fermat Prime 2^(2^n) + 1. To your third question: Yes. This is so, because 6 * 6 = 36 = 6 (mod 10) and the residue of a product or sum won't change if you reduce the factors / summands to their residues before multiplying / adding them. Benjamin

2003-06-09, 09:58	#13
TTn 2²×3³×59 Posts	Please dont recommend PFGW, to a novice user. Besides it is much slower than LLR, please see http://groups.yahoo.com/group/openpfgw/message/374 LLR is a generalized mersenne test for primes of the form (k*2^n-1) Come join us at the 15k search forum here. ;)

2003-06-09, 15:52	#14
clowns789 Jun 2003 The Computer 610₈ Posts	So I guess you might as well do the old 2^p-1 so it would go the fastest. I was thinking with the 2^p+1 and 16^p+1 you can find all three types of primes (regular, Mersenne, and Fermat) that you wouldn't with 2^p-1.