
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:  3853775193 · 2^{80001} + 1 
Verification status (*):  Proven 
Official Comment:  Cunningham chain 2nd kind (2p1) 
Proofcode(s): (*):  L109 : Nair, NewPGen, LLR 
Decimal Digits:  24093 (log_{10} is 24092.286569491) 
Rank (*):  60309 (digit rank is 4) 
Entrance Rank (*):  23953 
Currently on list? (*):  no 
Submitted:  5/6/2007 01:14:24 CDT 
Last modified:  5/6/2007 03:25:10 CDT 
Database id:  80350 
Status Flags:  none 
Score (*):  35.1619 (normalized score 0.0001) 

Archival tags:
There are certain forms classed as
archivable: these prime may (at times)
remain on this list even if they do not make
the Top 5000 proper. Such primes are tracked with archival
tags.
 Cunningham Chains (2nd kind) (archivable class *)
 Prime on list: no, rank 12, weight 34.8840970908708
Subcategory: "Cunningham chain 2nd kind (2p1)"
(archival tag id 212409, tag last modified 20160315 13:57:15)
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  80350 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/TrialDiv/TrialDiv q 3853775193 2 80001 1 2>&1 [Elapsed time: 8.609 seconds]

modified  20070530 21:58:14 
created  20070506 01:23:01 
id  89804 

field  value 
prime_id  80350 
person_id  9 
machine  RedHat P4 P4 
what  prime 
notes  Command: /home/caldwell/client/pfgw t q"3853775193*2^80001+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3853775193*2^80001+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(10240,21) to FFT(10240,20) Reduced from FFT(10240,20) to FFT(10240,19) Reduced from FFT(10240,19) to FFT(10240,18) Reduced from FFT(10240,18) to FFT(10240,17) Reduced from FFT(10240,17) to FFT(10240,16) 160074 bit request FFT size=(10240,16) Calling BrillhartLehmerSelfridge with factored part 99.96% 3853775193*2^80001+1 is prime! (58.8900s+0.0000s) [Elapsed time: 60 seconds]

modified  20070530 21:58:14 
created  20070506 03:24:10 
id  89811 

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
