2181229658912 · 4801# - 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:	2181229658912 · 4801# - 1
Verification status (*):	Proven
Official Comment (*):	Cunningham chain (4p+3)
Proof-code(s): (*):	p364 : Batalov, NewPGen, OpenPFGW
Decimal Digits:	2065 (log₁₀ is 2064.2391342057)
Rank (*):	109224 (digit rank is 7)
Entrance Rank (*):	109155
Currently on list? (*):	no
Submitted:	7/31/2026 22:50:02 UTC
Last modified:	8/8/2026 14:37:27 UTC
Database id:	142389
Status Flags:	none
Score (*):	27.5357 (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: no, rank 37, weight 34.952111677094
Subcategory: "Cunningham chain (4p+3)"
(archival tag id 240381, tag last modified 2026-08-08 14:37:31)

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 142389

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"2181229658912*4801#-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 2181229658912*4801#-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 4813, base 1+sqrt(4813)
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6858-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 4586/24710 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 4813, base 1+sqrt(4813)
Generic modular reduction using generic reduction FMA3 FFT length 768 on A 6858-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.48%

2181229658912*4801#-1 is prime! (2.2079s+0.0004s)
[Elapsed time: 5.00 seconds]

modified 2026-08-08 14:06:17

created 2026-08-08 14:06:12

id 188573

field	value
prime_id	142389
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"21812296589124801#-1" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 21812296589124801#-1 [N+1, Brillhart-Lehmer-Selfridge] trial Running N+1 test using discriminant 4813, base 1+sqrt(4813) Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6858-bit number Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 4586/24710 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 4813, base 1+sqrt(4813) Generic modular reduction using generic reduction FMA3 FFT length 768 on A 6858-bit number Calling Brillhart-Lehmer-Selfridge with factored part 33.48% 2181229658912*4801#-1 is prime! (2.2079s+0.0004s) [Elapsed time: 5.00 seconds]
modified	2026-08-08 14:06:17
created	2026-08-08 14:06:12
id	188573

Query times: 0.0006 seconds to select prime, 0.0008 seconds to seek comments.