89595955370432 · 2371# - 1

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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:	89595955370432 · 2371# - 1
Verification status (*):	Proven
Official Comment (*):	Cunningham chain (32p+31)
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	p364 : Batalov, NewPGen, OpenPFGW
Decimal Digits:	1017 (log₁₀ is 1016.7024710987)
Rank (*):	127941 (digit rank is 5)
Entrance Rank (*):	109118
Currently on list? (*):	short
Submitted:	3/25/2015 04:58:45 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	119628
Status Flags:	none
Score (*):	25.3238 (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.

Cunningham Chains (1st kind) (archivable class *)
Prime on list: yes, rank 1, weight 52.081094275039
Subcategory: "Cunningham chain (32p+31)"
(archival tag id 217960, tag last modified 2023-03-11 15:53:59)

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.

Serge Batalov writes (1 Apr 2015): (report abuse)

This is the first known titanic Cunningham Chain of length six.
Found as a subsequence of a (lot of) sieved candidate chains of length eight; starting testing from the middle, one gets three chances to win in this "lottery", yet the stream of candidates is not yet prohibitively thin.

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 119628

person_id 9

machine Using: Xeon 4c+4c 3.5GHz

what prime

notes Command: /home/caldwell/client/pfgw/pfgw64 -tp -q"89595955370432*2371#-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 89595955370432*2371#-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 2393, base 1+sqrt(2393) Calling Brillhart-Lehmer-Selfridge with factored part 33.43% 89595955370432*2371#-1 is prime! (0.5709s+0.0004s) [Elapsed time: 0.00 seconds]

modified 2020-07-07 22:30:17

created 2015-03-25 05:01:02

id 165233

field	value
prime_id	119628
person_id	9
machine	Using: Xeon 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/client/pfgw/pfgw64 -tp -q"895959553704322371#-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 895959553704322371#-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 2393, base 1+sqrt(2393) Calling Brillhart-Lehmer-Selfridge with factored part 33.43% 89595955370432*2371#-1 is prime! (0.5709s+0.0004s) [Elapsed time: 0.00 seconds]
modified	2020-07-07 22:30:17
created	2015-03-25 05:01:02
id	165233

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