
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^{102435} + 1)^{2}  2 
Verification status (*):  Proven 
Official Comment:  
Proofcode(s): (*):  p126 : Minovic, MultiSieve, OpenPFGW 
Decimal Digits:  61673 (log_{10} is 61672.0152116798) 
Rank (*):  49024 (digit rank is 1) 
Entrance Rank (*):  1222 
Currently on list? (*):  no 
Submitted:  2/23/2004 06:57:27 CDT 
Last modified:  2/23/2004 06:57:27 CDT 
Removed (*):  11/17/2005 15:58:38 CDT 
Database id:  68943 
Status Flags:  none 
Score (*):  38.0643 (normalized score 0.0025) 

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  68943 
person_id  9 
machine  Linux P4 2.8GHz 
what  prime 
notes  Command: /home/caldwell/client/pfgw f tc q"(2^102435+1)^22" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^102435+1)^22 [N1/N+1, BrillhartLehmerSelfridge] trial factoring to 20329733 Running N1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409750 bit request FFT size=(28672,16) Running N1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409750 bit request FFT size=(28672,16) Running N+1 test using discriminant 17, base 1+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409758 bit request FFT size=(28672,16) Running N+1 test using discriminant 17, base 2+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409758 bit request FFT size=(28672,16) Running N+1 test using discriminant 17, base 3+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409758 bit request FFT size=(28672,16) Running N+1 test using discriminant 17, base 4+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409758 bit request FFT size=(28672,16) Calling N+1 BLS with factored part 50.00% and helper 0.01% (150.01% proof) (2^102435+1)^22 is prime! (871.0246s+0.0000s)

modified  20040304 09:24:08 
created  20040223 07:23:01 
id  73895 

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.
