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 2007-03-14, 22:00 #1 maxal     Feb 2005 22·32·7 Posts primality of ((p+1)^p-1)/p^2 Is there any fast method (or software) to prove primality of numbers of the form N(p) = ((p+1)^p-1)/p^2 ? In particular, I am interested in proving that N(4357) is prime.
2007-03-14, 22:05   #2
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 Originally Posted by maxal Is there any fast method (or software) to prove primality of numbers of the form N(p) = ((p+1)^p-1)/p^2 ? In particular, I am interested in proving that N(4357) is prime.
ECPP works in polynomial time......

2007-03-14, 23:16   #3
maxal

Feb 2005

3748 Posts

Quote:
 Originally Posted by R.D. Silverman ECPP works in polynomial time......
The proof records of ECPP (at ECPP homepage) are about 2,500 decimal digits.
N(4357) has more than 15,000 decimal digits...

 2007-03-15, 14:56 #4 paulunderwood     Sep 2002 Database er0rr 3,533 Posts 20,562 digits or monoprocessor it is: 7,993 digits Last fiddled with by paulunderwood on 2007-03-15 at 15:05
 2007-03-16, 09:31 #5 armstrong1     Mar 2006 22 Posts N(4357) is prime,and it has 15850 digits !
 2007-03-16, 10:45 #6 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts armstrong1, how did you prove that? Alex
 2007-03-17, 01:44 #7 armstrong1     Mar 2006 22 Posts oh,i compute it in maple 10 -the software !
 2007-03-17, 04:36 #8 paulunderwood     Sep 2002 Database er0rr 353310 Posts Do you have a reference to the so-called proving algorithm used?
 2007-03-19, 06:20 #9 armstrong1     Mar 2006 22 Posts oh, no, i just compute it !
 2007-03-19, 13:01 #10 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts Are you certain that Maple used a primality proving algorithm, not just a probable primality testing algorithm? Which Maple function specifically did you use to test primality of this number? Alex
 2007-03-19, 14:23 #11 m_f_h     Feb 2007 24×33 Posts Conjecture: N(n)=0 mod M(n) for n=2^k-1. But N(66^2+1) You must have a powerful machine to use Maple's isprime() on that number... (on my laptop it takes too long :-( !) However, no factor below 2^32... (pari's default primelimit...)

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