
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:  Phi(5655, 34120)/(64772371 · 35066801243156348783521) 
Verification status (*):  PRP 
Official Comment:  ECPP 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  c54 : Wu_T, Primo 
Decimal Digits:  12155 (log_{10} is 12154.371966521) 
Rank (*):  69703 (digit rank is 2) 
Entrance Rank (*):  52260 
Currently on list? (*):  no 
Submitted:  9/1/2011 14:53:37 CDT 
Last modified:  9/1/2011 15:50:25 CDT 
Database id:  101438 
Status Flags:  Verify 
Score (*):  33.0446 (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.
 Elliptic Curve Primality Proof (archivable *)
 Prime on list: no, rank 71
Subcategory: "ECPP"
(archival tag id 213408, tag last modified 20161220 20:50:34)
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  101438 
person_id  9 
machine  Ditto P4 P4 
what  trial_divided 
notes  Command: /home/ditto/client/pfgw o f q"Phi(5655,34120)/(64772371*35066801243156348783521)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Phi(5655,34120)/....243156348783521) 1/1 mro=0
trial factoring to 3547487 Phi(5655,34120)/(64772371*3506680124...6348783521) has no small factor. [Elapsed time: 3.818 seconds]

modified  20111227 16:48:29 
created  20110901 15:05:01 
id  132442 

field  value 
prime_id  101438 
person_id  9 
machine  RedHat Virtual STEM Server 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"Phi(5655,34120)/(64772371*35066801243156348783521)" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing Phi(5655,34120)/(64772371*3506680124...6348783521) [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 2 Running N1 test using base 3 Running N1 test using base 7 Running N+1 test using discriminant 19, base 18+sqrt(19) Calling N1 BLS with factored part 0.08% and helper 0.00% (0.24% proof) Phi(5655,34120)/(64772371*3506680124...6348783521) is Fermat and Lucas PRP! (40.2708s+0.0131s) [Elapsed time: 40.00 seconds]

modified  20111227 16:48:29 
created  20110901 15:22:30 
id  132444 

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