Group, I believe that if 'N' passes the 2-PRP test that either 3, 5, or 7 divides 'N-1', one or all of them, or 'N' will be divisible by 3, 5, or 7 and be...
21295
Paul Leyland
xilmanuk
Feb 1, 2010 2:39 pm
Aargh! I misunderstood the example and posted complete claptrap. My apologies. To make amends: all Fermat numbers pass the 2-PRP test. Many composite ...
21296
Bill Bouris
leavemsg1
Feb 1, 2010 2:45 pm
forwarded... ... From: Bill Bouris <leavemsg1@...> To: Paul Leyland <paul@...> Sent: Mon, February 1, 2010 8:42:15 AM Subject: Re: {Spam?}...
21297
Paul Leyland
xilmanuk
Feb 1, 2010 2:54 pm
If you used your elderly computer to search for known results rather than for computations you would have discovered ...
21298
djbroadhurst
Feb 1, 2010 5:49 pm
... n = 1097343303233 is not prime n is 2-PRP n is 3-PRP n is coprime to 3*5*7 n-1 is coprime to 3*5*7 There are 95 such counterexamples in ...
21299
Bill Bouris
leavemsg1
Feb 1, 2010 7:00 pm
Here's how I want to define the magnum 357 test! take N; if 'N' passes the 2-PRP test, then... if 3, 5, or 7 divides 'N', then 'N' is composite... and we are...
21300
Jack Brennen
jbrennen
Feb 1, 2010 7:33 pm
Try N = 25326001. Try N = 3215031751. Then fix the test to handle those correctly. :)...
21301
djbroadhurst
Feb 2, 2010 12:27 am
... It takes less than 2 seconds to prove that there are at least 124880 counterexamples with N < 10^15. See: ...
21302
djbroadhurst
Feb 2, 2010 3:35 pm
... In less than 20 seconds, I found 993305 counterexamples in tables from William Galway and Richard Pinch. There are 319226 numbers N < 10^15 that are 2-PSP...
21303
Kermit Rose
kermit1941
Feb 4, 2010 8:35 pm
If p is prime, there exist an element g such that g**(p-1) = 1 mod p, and for 0 < k < (p-1), g**k is not = 1 mod p. g is called a generator mod p. I don't know...
21304
Kermit Rose
kermit1941
Feb 6, 2010 3:25 am
The quadratic part of the quadratic sieve factoring algorithm illustrated with a small integer. Let z = 33 = 3 * 11 We know that it is trivial to factor such a...
21305
Sren
srentospace
Feb 6, 2010 10:07 pm
Does anybody know how to get more digits in qbasic, or do I need another program....
21306
Di Maria Giovanni
calimero22
Feb 6, 2010 10:13 pm
You must use a good programming language: - use C language with GMP library to get unlimited digits.- Freebasic with GMP library to get unlimited digit.-...
21307
rupert.wood@...
rupert.wood...
Feb 8, 2010 11:59 pm
I have confirmed that the list for 10^8 "failures"; below 1000 also holds for values below 10^9....
21308
ianredwood
Feb 10, 2010 8:26 pm
Hi, What's the highest known n for which, for all 7 <= k <= n, pi(n/2) > pi(n) - pi(n/2)? Thankyou....
21309
Sren
srentospace
Feb 10, 2010 8:50 pm
Thanks for the advice using Ubasic, it needs my demands. I have calculated some formulas for n^2-n+p to relate to p=41, and as somebody said, it is trivial to...
21310
ianredwood
Feb 10, 2010 9:39 pm
Whoops - I've got to say that again. What's the highest known n for which, for any 7 <= k <= n, pi(k/2) > pi(k) - pi(k/2)? Is it bigger than 10^(60)?...
21311
maximilian_hasler
maximilian_h...
Feb 11, 2010 2:25 pm
... pi(k/2) > pi(k) - pi(k/2) <=> pi(k/2)*2 > pi(k) The function pi(k/2)*2 - pi(k) tends to infinity in view of the asymptotic behavious of the pi() function...
21312
ianredwood
Feb 11, 2010 4:19 pm
... Many thanks but the 'vector' part is beyond me. How do you know that the bounds are the ones, 5 and 21, that you cite? Can you supply any literary...
21313
alpertron
Feb 11, 2010 5:51 pm
Tapio Rajula posted a few days ago in http://www.mersenneforum.org/showthread.php?t=13051 <http://www.mersenneforum.org/showthread.php?t=13051> (Mersenne...
21314
maximilian_hasler
maximilian_h...
Feb 11, 2010 5:53 pm
... (...) ... It was mainly meant as illustration... among others, of the fact that I don't understand your k >= 7 lower limit... Could you first explain that...
21315
Maximilian Hasler
maximilian_h...
Feb 11, 2010 6:40 pm
... x ≥ 355991 according to the WP page. And I plotted the difference up to 10^6, there's really absolutely no doubt for smaller values ! M. [Non-text...
21316
Chris Caldwell
primemogul
Feb 11, 2010 6:45 pm
To add some context: F_14 = 2^(2^14)+1 was shown to be composite in 1963 by John Selfridge and Alexander Hurwitz. It took two-score and seven years to...
21317
Pavlos S
pavlos199
Feb 11, 2010 9:05 pm
Indeed, this is a remarkable discovery!Congratulations for the finding. ... From: Chris Caldwell <caldwell@...> Subject: RE: [PrimeNumbers] First known...
21318
djbroadhurst
Feb 12, 2010 11:45 pm
... Thanks, Dario, for communicating Tapio Rajala's grand discovery. I remark that http://www.prothsearch.net/fermat.html is still consistent with the (to me,...
21319
djbroadhurst
Feb 13, 2010 2:32 pm
... I'm happy to report that OpenPFGW discovered and proved that ... At 512775 digits, it seems to occupy second place in the "neither base-2 nor GF" league,...
21320
jpyah2001
Feb 13, 2010 3:31 pm
Nice result!! I shall verify it using LLR 3.8.0 Congratulations to you and to OpenPFGW developpers! Jean...
21321
djbroadhurst
Feb 13, 2010 8:37 pm
... Thanks, Jean. I had been hoping for just such a "mega-trit" prime. David, pp SCRUB, Society for the Comfort and Relief of Underprivileged Bases ...
21322
djbroadhurst
Feb 13, 2010 9:49 pm
... Update: a second mega-trit has popped up as 3-PRP, just nearby. Seems like a lucky weekend, as long as OpenPFGW is behaving. The N-1 BLS test is now in...
21323
djbroadhurst
Feb 13, 2010 11:36 pm
... One witness seemed to be enough this time: Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2*3^1086112+1 is...
