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:||278 · 315180134 + 1|
|Verification status (*):||Proven|
|Proof-code(s): (*):||L1471 : Gunn, Srsieve, CRUS, LLR|
|Decimal Digits:||450034 (log10 is 450033.117341132)|
|Rank (*):||5000 (digit rank is 1)|
|Entrance Rank (*):||1660|
|Currently on list? (*):||yes|
|Submitted:||6/13/2015 02:39:39 CDT|
|Last modified:||6/13/2015 03:20:30 CDT|
|Score (*):||44.1816 (normalized score 1)|
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||Using: Xeon 4c+4c 3.5GHz|
|notes||Command: /home/caldwell/client/pfgw/pfgw64 -t -q"278*315^180134+1" 2>&1|
PFGW Version 18.104.22.168BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 278*315^180134+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 38.20%
278*315^180134+1 is prime! (1343.8980s+0.0128s)
[Elapsed time: 22.40 minutes]
Query times: 0.0017 seconds to select prime, 0.0005 seconds to seek comments.