
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:  3 · 100000845^{8192} + 3 · 100000845^{4096} + 1 
Verification status (*):  Proven 
Official Comment:  
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  p97 : Andersen, OpenPFGW 
Decimal Digits:  65537 (log_{10} is 65536.507184034) 
Rank (*):  45106 (digit rank is 2) 
Entrance Rank (*):  4688 
Currently on list? (*):  no 
Submitted:  1/7/2006 21:45:26 CDT 
Last modified:  1/7/2006 23:21:31 CDT 
Removed (*):  2/14/2006 06:13:49 CDT 
Database id:  76705 
Status Flags:  none 
Score (*):  38.2517 (normalized score 0.0041) 

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  76705 
person_id  9 
machine  Linux P4 2.8GHz 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f q"3*100000845^8192+3*100000845^4096+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 21696196 3*100000845^8192+3*100000845^4096+1 has no small factor. [Elapsed time: 145.374 seconds]

modified  20060118 12:45:08 
created  20060107 21:52:00 
id  82385 

field  value 
prime_id  76705 
person_id  9 
machine  Linux P4 2.8GHz 
what  prime 
notes  Command: /home/caldwell/client/pfgw t q"3*100000845^8192+3*100000845^4096+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3*100000845^8192+3*100000845^4096+1 [N1, BrillhartLehmerSelfridge] 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) 435424 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) 435424 bit request FFT size=(28672,16) Running N1 test using base 13 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) 435424 bit request FFT size=(28672,16) Running N1 test using base 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) 435424 bit request FFT size=(28672,16) Calling BrillhartLehmerSelfridge with factored part 40.35% 3*100000845^8192+3*100000845^4096+1 is prime! (1773.7773s+0.0100s) [Elapsed time: 5310 seconds]

modified  20060118 12:45:08 
created  20060107 21:53:01 
id  82386 

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
