2¹¹⁶²²⁴ - 15905

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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:	2¹¹⁶²²⁴ - 15905
Verification status (*):	PRP
Official Comment (*):	ECPP
Proof-code(s): (*):	c87 : Kaiser1, OpenPFGW, Primo
Decimal Digits:	34987 (log₁₀ is 34986.910216051)
Rank (*):	65908 (digit rank is 1)
Entrance Rank (*):	56250
Currently on list? (*):	no
Submitted:	11/17/2017 05:38:42 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	123996
Status Flags:	Verify
Score (*):	36.3148 (normalized score 0.0001)

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 24
Subcategory: "ECPP"
(archival tag id 218920, tag last modified 2023-12-16 03:37:30)

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 123996

person_id 9

machine Using: Xeon (pool) 4c+4c 3.5GHz

what prp

notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"2^116224-15905" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 2^116224-15905 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 31, base 1+sqrt(31) Calling N+1 BLS with factored part 0.08% and helper 0.02% (0.25% proof) 2^116224-15905 is Fermat and Lucas PRP! (36.2883s+0.0002s) [Elapsed time: 37.00 seconds]

modified 2020-07-07 22:30:15

created 2017-11-17 05:43:01

id 169659

field	value
prime_id	123996
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prp
notes	Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"2^116224-15905" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 2^116224-15905 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 31, base 1+sqrt(31) Calling N+1 BLS with factored part 0.08% and helper 0.02% (0.25% proof) 2^116224-15905 is Fermat and Lucas PRP! (36.2883s+0.0002s) [Elapsed time: 37.00 seconds]
modified	2020-07-07 22:30:15
created	2017-11-17 05:43:01
id	169659

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

2116224 - 15905

This prime's information:

Archival tags:

Verification data:

2¹¹⁶²²⁴ - 15905