10^2718281 - 5 · 10^1631138 - 5 · 10^1087142 - 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:	10^2718281 - 5 · 10^1631138 - 5 · 10^1087142 - 1
Verification status (*):	Proven
Official Comment (*):	Palindrome
Unofficial Comments:	This prime has 2 user comments below.
Proof-code(s): (*):	p423 : Propper, Batalov, EMsieve, OpenPFGW
Decimal Digits:	2718281 (log₁₀ is 2718281)
Rank (*):	183 (digit rank is 1)
Entrance Rank (*):	157
Currently on list? (*):	yes
Submitted:	8/6/2024 21:25:13 UTC
Last modified:	8/17/2024 00:37:10 UTC
Database id:	138383
Status Flags:	none
Score (*):	49.699 (normalized score 96.7171)

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.

Palindrome (archivable *)
Prime on list: yes, rank 1
Subcategory: "Palindrome"
(archival tag id 229624, tag last modified 2024-08-17 00:37:12)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
Serge Batalov writes (7 Aug 2024): (report abuse)
For N+1 proof, use -a1 option (standard FFT size will exceed error limit), -tp, and -f1.
pfgw -T80 -a1 -V -N -f1 -l -tp ../p
PFGW Version 4.1.3.64BIT.20240114.x86_Dev [GWNUM 30.19]

Output logging to file pfgw.out
Factoring numbers to 1% of normal.

Primality testing 10^2718281-5*10^1631138-5*10^1087142-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 17, base 1+sqrt(17)
Generic modular reduction using Montgomery reduction AVX-512 FFT length 2x504K, Pass1=1152, Pass2=448, clm=2, 28 threads on A 9029935-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 39.99%
10^2718281-5*10^1631138-5*10^1087142-1 is prime! (64285.1622s+0.0425s)
Jeppe Stig Nielsen writes (7 Aug 2024): (report abuse)

With PFGW, one can possibly use -e6 (instead of -f1) to only factor to depth p=5.

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 138383

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"10^2718281-5*10^1631138-5*10^1087142-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 10^2718281-5*10^1631138-5*10^1087142-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 17, base 1+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 960K, Pass1=1536, Pass2=640, clm=1 on A 9029935-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 636693/9029941 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 17, base 1+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 1000K, Pass1=640, Pass2=1600, clm=2 on A 9029935-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 13421/9029941 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a2 (or possibly -a0) switch)
Running N+1 test using discriminant 17, base 1+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 1008K, Pass1=192, Pass2=5376, clm=4 on A 9029935-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 39.99%

10^2718281-5*10^1631138-5*10^1087142-1 is prime! (724893.3142s+0.0378s)
[Elapsed time: 8.39 days]

modified 2024-08-16 23:58:20

created 2024-08-08 14:36:45

id 184225

field	value
prime_id	138383
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"10^2718281-510^1631138-510^1087142-1" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 10^2718281-510^1631138-510^1087142-1 [N+1, Brillhart-Lehmer-Selfridge] trial Running N+1 test using discriminant 17, base 1+sqrt(17) Generic modular reduction using generic reduction AVX-512 FFT length 960K, Pass1=1536, Pass2=640, clm=1 on A 9029935-bit number Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 636693/9029941 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 17, base 1+sqrt(17) Generic modular reduction using generic reduction AVX-512 FFT length 1000K, Pass1=640, Pass2=1600, clm=2 on A 9029935-bit number Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 13421/9029941 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a2 (or possibly -a0) switch) Running N+1 test using discriminant 17, base 1+sqrt(17) Generic modular reduction using generic reduction AVX-512 FFT length 1008K, Pass1=192, Pass2=5376, clm=4 on A 9029935-bit number Calling Brillhart-Lehmer-Selfridge with factored part 39.99% 10^2718281-510^1631138-510^1087142-1 is prime! (724893.3142s+0.0378s) [Elapsed time: 8.39 days]
modified	2024-08-16 23:58:20
created	2024-08-08 14:36:45
id	184225

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

102718281 - 5 · 101631138 - 5 · 101087142 - 1

This prime's information:

Archival tags:

User comments about this prime (disclaimer):

Verification data:

10^2718281 - 5 · 10^1631138 - 5 · 10^1087142 - 1