Copeland-Erdos Constant Primes - Page 2

Batalov · 2015-12-12, 00:13

ok (for independence sake, constructed it with gp from scratch)
...running a 2-PRP test now...
...done
Generic modular reduction using generic reduction FMA3 FFT length 96K, Pass1=384, Pass2=256 on A 971486-bit number
2357111317...619511619537619543619561619 is 2-PRP! (3880.7502s+4.8723s)
...running a 11-PRP test now...
...done
Generic modular reduction using generic reduction FMA3 FFT length 96K, Pass1=384, Pass2=256 on A 971486-bit number
2357111317...619511619537619543619561619 is 11-PRP! (3552.4437s+2.4134s)

paulunderwood · 2015-12-12, 01:04

Please attach the decimal representation of the PRP

rogue · 2015-12-12, 02:02

Quote:

Originally Posted by Batalov

ok (for independence sake, constructed it with gp from scratch)
...running a 2-PRP test now...
...done
2357111317...19511619537619543619561619 is 2-PRP! (3880.7502s+4.8723s)

Thank you Serge!

paulunderwood · 2015-12-12, 03:03

Thanks for the attachment, Serge. After about 50 mins using 80% of a 3.5GHz core, my GWNUM based program (using a=0, since Jacobi(-1,n)==-1) reports "Likely prime!" meaning (x+2)^(n+1)==5 (mod n, x^2+1).

rogue · 2015-12-12, 13:36

Quote:

Originally Posted by paulunderwood

Thanks for the attachment, Serge. After about 50 mins using 80% of a 3.5GHz core, my GWNUM based program (using a=0, since Jacobi(-1,n)==-1) reports "Likely prime!" meaning (x+2)^(n+1)==5 (mod n, x^2+1).

Thanks to you as well Paul!

ericw · 2015-12-17, 11:50

Quote:

Originally Posted by rogue

If I've written my code correctly then CE(292447) is PRP. Even if my code isn't correct, it is a fairly large PRP. Could someone please independently verify?

Verified also using Mathematica's PrimeQ (returns True -> probable prime)

Congratulations!

rogue · 2015-12-17, 12:07

Quote:

Originally Posted by ericw

Verified also using Mathematica's PrimeQ (returns True -> probable prime)

Congratulations!

How long did that take?

fivemack · 2015-12-17, 12:54

I am confused about the decimal representation, it seems to stop half-way through a number

619511
619537
619543
619561
619

I had thought you were looking at the number as a series of concatenated primes, rather than as a digit-string (made up of concatenated primes) whose prefixes you were testing for primality.

R. Gerbicz · 2015-12-17, 14:31

Quote:

Originally Posted by rogue

How long did that take?

Couldn't be that too slow as Mathematica is using gmp: http://www.wolfram.com/LGPL/GMP/ .

rogue · 2015-12-17, 14:32

Quote:

Originally Posted by fivemack

I am confused about the decimal representation, it seems to stop half-way through a number

619511
619537
619543
619561
619

I had thought you were looking at the number as a series of concatenated primes, rather than as a digit-string (made up of concatenated primes) whose prefixes you were testing for primality.

No. You are thinking about the Smarandache-Wellin search.

ericw · 2015-12-21, 13:56

Quote:

Originally Posted by rogue

How long did that take?

32 CPU-hours on moderately old hardware. (PrimeQ uses a multiple Rabin-Miller test in bases 2 and 3 combined with a Lucas pseudoprime test.)

2015-12-12, 03:03	#15
paulunderwood Sep 2002 Database er0rr 3739₁₀ Posts	Thanks for the attachment, Serge. After about 50 mins using 80% of a 3.5GHz core, my GWNUM based program (using a=0, since Jacobi(-1,n)==-1) reports "Likely prime!" meaning (x+2)^(n+1)==5 (mod n, x^2+1). Last fiddled with by paulunderwood on 2015-12-12 at 03:04

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2015-12-12, 01:04	#13
paulunderwood Sep 2002 Database er0rr 3,739 Posts	Please attach the decimal representation of the PRP

2015-12-17, 12:54	#19
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 7²·131 Posts	I am confused about the decimal representation, it seems to stop half-way through a number 619511 619537 619543 619561 619 I had thought you were looking at the number as a series of concatenated primes, rather than as a digit-string (made up of concatenated primes) whose prefixes you were testing for primality.