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:
|Description:||4847 · 23321063 + 1|
|Verification status (*):||Proven|
|Proof-code(s): (*):||SB9 : Hassler, SoBSieve, ProthSieve, Ksieve, PRP, Proth.exe, SB|
|Decimal Digits:||999744 (log10 is 999743.265962827)|
|Rank (*):||412 (digit rank is 1)|
|Entrance Rank (*):||9|
|Currently on list? (*):||short|
|Submitted:||10/21/2005 13:14:33 CDT|
|Last modified:||10/21/2005 13:14:33 CDT|
|Score (*):||46.6322 (normalized score 15.2973)|
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.
|machine||RedHat P4 P4|
|notes||Command: /home/caldwell/client/pfgw -t -q"4847*2^3321063+1" 2>&1|
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 4847*2^3321063+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(458752,19) to FFT(458752,18)
Reduced from FFT(458752,18) to FFT(458752,17)
Reduced from FFT(458752,17) to FFT(458752,16)
6642160 bit request FFT size=(458752,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
4847*2^3321063+1 is prime! (-1915.2378s+0.0000s)
[Elapsed time: 26.91 hours]
Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.