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Old 2007-03-27, 18:40   #1
nuggetprime's Avatar
Mar 2007

12E16 Posts
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Is there a coordinated partition prime search?
How they were calulated and sieved?
How they were proved?
Which ranges are currently tested and which are not tested?

Hope that somebody could answer the one or the other question.

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Old 2007-03-30, 18:22   #2
Jens K Andersen
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Feb 2006

2×5×23 Posts

There are no answers so I will say what I know.
The top-20 partition primes are at I don't think there is any coordination. You could ask the discoverers if you want to be sure.
They were all proved with Marcel Martin's Primo. Some used PrimeForm for prp testing, some mention no prp program. Primality proofs are the hardest part for partition primes. I have not heard of anybody who records large prp partition numbers. There are probably huge gaps in the partition numbers which have been prp tested (or have been computed). If you pick an interval far away from the reported primes then it probably hasn't been tested.

I found the partition prime p(10020010) in 2005 when it was the record. I trial factored to 23 (yes: twenty three) with my own unpublished program, as mentioned in The PARI/GP function numbpart (I don't know its algorithm) then computed the partition numbers which had no factor <= 23. PrimeForm trial factored them from 23 and made prp tests (but I didn't include it in the prover code because it was computationally insignificant compared to the primality proof).
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Old 2007-04-04, 15:16   #3
davieddy's Avatar
Dec 2006

145128 Posts

Is it too late to insert an "i" into the title of this thread?
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Old 2007-04-04, 15:39   #4
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Aug 2002

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Is it too late to insert an "i" into the title of this thread?
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