PRP Records Probable Primes Top 10000
PRP RecordsProbable Primes Top 10000
(300809 PRPs in the top)
What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
http://www.primenumbers.net/prptop/prptop.php
比如
(10^8177207-1)/9这个大整数有8177207位，很可能是素数！ 来自网页
https://t5k.org/primes/download.php
https://t5k.org/primes/lists/all.txt
THE LARGEST KNOWN PRIMES
(The 5,000 largest known primes)
(selected smaller primes which have comments are included)
Originally Compiled by Samuel Yates -- Continued by Chris Caldwell and now maintained by Reginald McLean
(Mon Jan 20 04:38:06 UTC 2025)
So that I can maintain this database of the 5,000 largest known primes
(plus selected smaller primes with 1,000 or more digits), please send
any new primes (that are large enough) to:
https://t5k.org/bios/submission.php
This list in a searchable form (plus information such as how to find
large primes and how to prove primality) is available at the interactive
web site:
https://t5k.org/primes/
See the last pages for information about the provers.
The letters after the rank refer to when the prime was submitted.
'a' is this month, 'b' last month... (10^8177207-1)/9hugecalc素数判定，这个数，需要多长时间？ 8177207位整数，他们都是怎么判定的？难道都是用超级计算机干的吗？
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