"10000000000000000000...(34053 other digits)...00000000000000532669"

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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 PrimePages database: 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:

Description:	"10000000000000000000...(34053 other digits)...00000000000000532669"
Verification status (*):	PRP
Official Comment (*):	ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	c84 : Underwood, Primo
Decimal Digits:	34093 (log₁₀ is 34092)
Rank (*):	66206 (digit rank is 1)
Entrance Rank (*):	55240
Currently on list? (*):	no
Submitted:	11/23/2016 14:03:47 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	122527
Blob database id:	359
Status Flags:	Verify
Score (*):	36.2347 (normalized score 0.0001)

Description: (from blob table id=359)

Arranged in a 103 by 331 grid this prime depicts the Mersenne prime exponent 57,885,161

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 27
Subcategory: "ECPP"
(archival tag id 218523, tag last modified 2023-12-16 03:37:30)

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.

Paul Underwood writes (24 Nov 2016): (report abuse)

Certificate Announcement and printable forms

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 122527

person_id 9

machine Using: Xeon 4c+4c 3.5GHz

what prp

notes Command: /home/caldwell/client/pfgw/pfgw64 -tc p_122527.txt 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 1000000000...0000532669 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N+1 BLS with factored part 0.05% and helper 0.02% (0.15% proof) 1000000000...0000532669 is Fermat and Lucas PRP! (92.2635s+0.0162s) [Elapsed time: 1.53 minutes]

modified 2020-07-07 22:30:16

created 2016-11-23 14:11:02

id 168168

field	value
prime_id	122527
person_id	9
machine	Using: Xeon 4c+4c 3.5GHz
what	prp
notes	Command: /home/caldwell/client/pfgw/pfgw64 -tc p_122527.txt 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 1000000000...0000532669 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N+1 BLS with factored part 0.05% and helper 0.02% (0.15% proof) 1000000000...0000532669 is Fermat and Lucas PRP! (92.2635s+0.0162s) [Elapsed time: 1.53 minutes]
modified	2020-07-07 22:30:16
created	2016-11-23 14:11:02
id	168168

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