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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:  (U(9275, 1, 3961) + U(9275, 1, 3960))/(U(9275, 1, 45) + U(9275, 1, 44)) 
Verification status (*):  PRP 
Official Comment:  Lehmer primitive part 
Unofficial Comments:  This prime has 2 user comments below. 
Proofcode(s): (*):  x38 : Broadhurst, Primo, OpenPFGW 
Decimal Digits:  15537 (log_{10} is 15536.001284243) 
Rank (*):  64648 (digit rank is 1) 
Entrance Rank (*):  35575 
Currently on list? (*):  short 
Submitted:  5/10/2009 04:19:03 CDT 
Last modified:  5/10/2009 04:50:21 CDT 
Database id:  88162 
Status Flags:  Verify 
Score (*):  33.8047 (normalized score 0) 

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.
 Lehmer primitive part (archivable *)
 Prime on list: yes, rank 7
Subcategory: "Lehmer primitive part"
(archival tag id 210442, tag last modified 20130205 17:20:28)
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  88162 
person_id  9 
machine  Ditto P4 P4 
what  trial_divided 
notes  Command: /home/ditto/client/pfgw o f q"(lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44))" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] (lucasU(9275,1,3961)+luca.........,1,45)+lucasU(92 1/1
trial factoring to 4623227 (lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44)) has no small factor. [Elapsed time: 6.252 seconds]

modified  20111227 16:48:44 
created  20090510 04:35:01 
id  105687 

field  value 
prime_id  88162 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"(lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44))" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44)) [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) 103228 bit request FFT size=(6144,17) Running N1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) 103228 bit request FFT size=(6144,17) Running N+1 test using discriminant 23, base 1+sqrt(23) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) 103236 bit request FFT size=(6144,17) Calling N1 BLS with factored part 0.57% and helper 0.29% (2.01% proof) (lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44)) is Fermat and Lucas PRP! (150.4400s+0.0100s) [Elapsed time: 2.77 minutes]

modified  20090525 07:25:55 
created  20090510 04:23:01 
id  105686 

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
