The Prime Database: 9867*2^381336+1

9867 · 2³⁸¹³³⁶ + 1
(Another of the Prime Pages' resources)

GIMPS has discovered a new largest known prime number: 2^82589933-1 (24,862,048 digits)

For this prime : General Information : Verification Data :

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help) value

Description: 9867 · 2³⁸¹³³⁶ + 1

Verification status (*): Proven

Official Comment:

Proof-code(s): (*): L635 : Vogel, Srsieve, PrimeGrid, LLR

Decimal Digits: 114798 (log₁₀ is 114797.56861165)

Rank (*): 37869 (digit rank is 1)

Entrance Rank (*): 4500

Currently on list? (*): no

Submitted: 3/12/2009 15:48:50 CDT

Last modified: 3/12/2009 16:20:18 CDT

Removed (*): 4/12/2009 16:51:21 CDT

Database id: 87080

Status Flags: none

Score (*): 39.9794 (normalized score 0.0188)

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 87080

person_id 9

machine RedHat P4 P4

what trial_divided

notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 9867 2 381336 1 2>&1
[Elapsed time: 9.100 seconds]

modified 2011-12-27 16:48:45

created 2009-03-12 15:52:02

id 103529

field value

prime_id 87080

person_id 9

machine RedHat P4 P4

what prime

notes Command: /home/caldwell/client/pfgw -t -q"9867*2^381336+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 9867*2^381336+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(49152,20) to FFT(49152,19)
Reduced from FFT(49152,19) to FFT(49152,18)
Reduced from FFT(49152,18) to FFT(49152,17)
Reduced from FFT(49152,17) to FFT(49152,16)
762708 bit request FFT size=(49152,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
9867*2^381336+1 is prime! (768.4700s+0.0000s)
[Elapsed time: 13.02 minutes]

modified 2009-03-24 13:31:30

created 2009-03-12 15:53:02

id 103530

Query times: 0.0001 seconds to select prime, 0.0003 seconds to seek comments.