78531447842897 · 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:	78531447842897 · 3727#/2 + 4
Verification status (*):	PRP
Official Comment (*):	Quintuplet (5)
Proof-code(s): (*):	E14 : Batalov, EMsieve, CM
Decimal Digits:	1605 (log₁₀ is 1604.5917128176)
Rank (*):	112586 (digit rank is 10)
Entrance Rank (*):	112577
Currently on list? (*):	yes
Submitted:	3/15/2026 20:20:08 UTC
Last modified:	3/16/2026 13:37:10 UTC
Database id:	142120
Status Flags:	Verify
Score (*):	26.7498 (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 (5)"
(archival tag id 240209, tag last modified 2026-03-16 13:37:12)

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 142120

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"78531447842897*3727#/2+4" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 78531447842897*3727#/2+4 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5331-bit number
Running N+1 test using discriminant 3733, base 96+sqrt(3733)
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5331-bit number
Calling N-1 BLS with factored part 0.34% and helper 0.06% (1.09% proof)

78531447842897*3727#/2+4 is Fermat and Lucas PRP! (0.1496s+0.0003s)
[Elapsed time: 5.00 seconds]

modified 2026-03-16 12:46:16

created 2026-03-16 12:46:11

id 188313

field	value
prime_id	142120
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"785314478428973727#/2+4" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 785314478428973727#/2+4 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 2 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5331-bit number Running N+1 test using discriminant 3733, base 96+sqrt(3733) Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5331-bit number Calling N-1 BLS with factored part 0.34% and helper 0.06% (1.09% proof) 78531447842897*3727#/2+4 is Fermat and Lucas PRP! (0.1496s+0.0003s) [Elapsed time: 5.00 seconds]
modified	2026-03-16 12:46:16
created	2026-03-16 12:46:11
id	188313

Query times: 0.0491 seconds to select prime, 0.0006 seconds to seek comments.