8349 · 2^6082397 - 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:	8349 · 2^6082397 - 1
Verification status (*):	Proven
Official Comment (*):	[none]
Proof-code(s): (*):	L4965 : Propper, LLR
Decimal Digits:	1830988 (log₁₀ is 1830987.8641711)
Rank (*):	443 (digit rank is 1)
Entrance Rank (*):	182
Currently on list? (*):	yes
Submitted:	8/17/2021 20:46:19 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	132628
Status Flags:	none
Score (*):	48.488 (normalized score 28.8118)

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 132628

person_id 9

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

what prime

notes Command: /home/caldwell/clientpool/4/pfgw64 -tp -q"8349*2^6082397-1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 8349*2^6082397-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 19/6082412 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 5, base 1+sqrt(5) Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 21/6082412 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a2 (or possibly -a0) switch) Running N+1 test using discriminant 5, base 1+sqrt(5) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 8349*2^6082397-1 is prime! (81292.9759s+0.0012s) [Elapsed time: 22.58 hours]

modified 2022-07-11 18:21:46

created 2021-08-17 20:51:02

id 178340

field	value
prime_id	132628
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/clientpool/4/pfgw64 -tp -q"83492^6082397-1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 83492^6082397-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 19/6082412 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 5, base 1+sqrt(5) Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 21/6082412 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a2 (or possibly -a0) switch) Running N+1 test using discriminant 5, base 1+sqrt(5) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 8349*2^6082397-1 is prime! (81292.9759s+0.0012s) [Elapsed time: 22.58 hours]
modified	2022-07-11 18:21:46
created	2021-08-17 20:51:02
id	178340

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.

8349 · 26082397 - 1

This prime's information:

Verification data:

8349 · 2^6082397 - 1