primality of ((p+1)^p-1)/p^2

maxal · 2007-03-14, 22:00

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.

R.D. Silverman · 2007-03-14, 22:05

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......

maxal · 2007-03-14, 23:16

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...

paulunderwood · 2007-03-15, 14:56

20,562 digits

or monoprocessor it is: 7,993 digits

armstrong1 · 2007-03-16, 09:31

N(4357) is prime,and it has 15850 digits !

akruppa · 2007-03-16, 10:45

armstrong1,

how did you prove that?

Alex

armstrong1 · 2007-03-17, 01:44

oh,i compute it in maple 10 -the software !

paulunderwood · 2007-03-17, 04:36

Do you have a reference to the so-called proving algorithm used?

armstrong1 · 2007-03-19, 06:20

oh, no, i just compute it !

akruppa · 2007-03-19, 13:01

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

m_f_h · 2007-03-19, 14:23

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...)

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.

2007-03-15, 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

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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...)