p(100077222)
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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:p(100077222)
Verification status (*):PRP
Official Comment:Partitions, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c59 : Metcalfe, OpenPFGW, Primo
Decimal Digits:11136   (log10 is 11135.5457736472)
Rank (*):72052 (digit rank is 2)
Entrance Rank (*):61120
Currently on list? (*):short
Submitted:11/4/2012 04:13:23 CDT
Last modified:11/5/2012 07:50:37 CDT
Database id:110049
Blob database id:286
Status Flags:Verify
Score (*):32.7734 (normalized score 0)

Description: (from blob table id=286)

The number of partitions of 100077222 is p(100077222).

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 104
Subcategory: "ECPP"
(archival tag id 214677, tag last modified 2017-10-14 12:20:20)
Partitions (archivable *)
Prime on list: yes, rank 20
Subcategory: "Partitions"
(archival tag id 214678, tag last modified 2017-10-14 12:20:22)

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.

David Metcalfe writes (11 Sep 2014): 
Certificate available from here.

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.
fieldvalue
prime_id110049
person_id9
machineDitto P4 P4
whattrial_divided
notesPFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
3513772562026429....0081930156844457 1/1 mro=0


trial factoring to 3227492
3513772562...0156844457 has no small factor.
[Elapsed time: 13.819 seconds]
modified2012-11-05 12:34:51
created2012-11-04 23:35:02
id150085

fieldvalue
prime_id110049
person_id9
machineDitto P4 P4
whatprp
notesPFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 3513772562...0156844457 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N+1 BLS with factored part 0.09% and helper 0.06% (0.33% proof)
3513772562...0156844457 is Fermat and Lucas PRP! (47.4760s+0.0037s)
[Elapsed time: 47.00 seconds]
modified2012-11-05 07:38:49
created2012-11-05 07:38:01
id150086

Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.