1932149198555 · 3727#/2 + 4

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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:	1932149198555 · 3727#/2 + 4
Verification status (*):	PRP
Official Comment (*):	Quintuplet (4)
Proof-code(s): (*):	E14 : Batalov, EMsieve, CM
Decimal Digits:	1603 (log₁₀ is 1602.9827098724)
Rank (*):	112365 (digit rank is 2)
Entrance Rank (*):	112326
Currently on list? (*):	yes
Submitted:	2/14/2026 20:56:57 UTC
Last modified:	2/15/2026 09:37:11 UTC
Database id:	141758
Status Flags:	Verify
Score (*):	26.7467 (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.

Quintuplet (archivable class *)
Prime on list: yes, rank 5
Subcategory: "Quintuplet (4)"
(archival tag id 239922, tag last modified 2026-02-15 09:37:13)

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 141758

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"1932149198555*3727#/2+4" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 1932149198555*3727#/2+4 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5325-bit number
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5325-bit number
Running N-1 test using base 11
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5325-bit number
Running N-1 test using base 19
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5325-bit number
Running N+1 test using discriminant 31, base 78+sqrt(31)
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5325-bit number
Calling N+1 BLS with factored part 0.11% and helper 0.04% (0.39% proof)

1932149198555*3727#/2+4 is Fermat and Lucas PRP! (0.1830s+0.0002s)
[Elapsed time: 5.00 seconds]

modified 2026-02-15 09:19:53

created 2026-02-15 09:19:48

id 187947

field	value
prime_id	141758
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"19321491985553727#/2+4" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 19321491985553727#/2+4 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 3 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5325-bit number Running N-1 test using base 7 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5325-bit number Running N-1 test using base 11 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5325-bit number Running N-1 test using base 19 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5325-bit number Running N+1 test using discriminant 31, base 78+sqrt(31) Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5325-bit number Calling N+1 BLS with factored part 0.11% and helper 0.04% (0.39% proof) 1932149198555*3727#/2+4 is Fermat and Lucas PRP! (0.1830s+0.0002s) [Elapsed time: 5.00 seconds]
modified	2026-02-15 09:19:53
created	2026-02-15 09:19:48
id	187947

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