
The nth Prime Page will now find any of the first 2,623,557,157,654,233 primes or
π( x) for x up to 100,000,000,000,000,000.
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes. This prime's information:
field (help)  value 
Description:  (2^{253987}  1)^{2}  2 
Verification status (*):  Proven 
Official Comment:  
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  p89 : Emmanuel, OpenPFGW 
Decimal Digits:  152916 (log_{10} is 152915.41101742) 
Rank (*):  29436 (digit rank is 1) 
Entrance Rank (*):  912 
Currently on list? (*):  no 
Submitted:  5/7/2007 15:02:47 CDT 
Last modified:  5/8/2007 00:56:25 CDT 
Removed (*):  6/3/2010 13:44:26 CDT 
Database id:  80384 
Status Flags:  none 
Score (*):  40.8622 (normalized score 0.0569) 

User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
Verification data:
The Top 5000 Primes is a list for proven primes only. In order to maintain the
integrity of this list, we seek to verify the primality of all submissions.
We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial
divide and PRP
check every entry before it is included in the list.
field  value 
prime_id  80384 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f q"(2^2539871)^22" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 53636202 (2^2539871)^22 has no small factor. [Elapsed time: 611.666 seconds]

modified  20070530 21:58:14 
created  20070507 15:22:13 
id  89880 

field  value 
prime_id  80384 
person_id  9 
machine  RedHat P4 P4 
what  prime 
notes  Command: /home/caldwell/client/pfgw tc q"(2^2539871)^22" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^2539871)^22 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015956 bit request FFT size=(65536,16) Running N+1 test using discriminant 11, base 2+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015964 bit request FFT size=(65536,16) Running N+1 test using discriminant 11, base 3+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015964 bit request FFT size=(65536,16) Running N+1 test using discriminant 11, base 4+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015964 bit request FFT size=(65536,16) Calling N+1 BLS with factored part 50.00% and helper 0.01% (150.02% proof) (2^2539871)^22 is prime! (1201.8184s+0.0200s) [Elapsed time: 34402 seconds]

modified  20070530 21:58:14 
created  20070507 15:23:03 
id  89881 

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
