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Old 2007-03-14, 22:00   #1
maxal
 
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Default 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.
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Old 2007-03-14, 22:05   #2
R.D. Silverman
 
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Quote:
Originally Posted by maxal View Post
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......
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Old 2007-03-14, 23:16   #3
maxal
 
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Quote:
Originally Posted by R.D. Silverman View Post
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...
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Old 2007-03-15, 14:56   #4
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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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Old 2007-03-16, 09:31   #5
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N(4357) is prime,and it has 15850 digits !
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Old 2007-03-16, 10:45   #6
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armstrong1,

how did you prove that?

Alex
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Old 2007-03-17, 01:44   #7
armstrong1
 
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oh,i compute it in maple 10 -the software !
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Old 2007-03-17, 04:36   #8
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Do you have a reference to the so-called proving algorithm used?
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Old 2007-03-19, 06:20   #9
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oh, no, i just compute it !
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Old 2007-03-19, 13:01   #10
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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
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Old 2007-03-19, 14:23   #11
m_f_h
 
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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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