301562 · 52408646 - 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 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:301562 · 52408646 - 1
Verification status (*):Proven
Official Comment:
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):L4675 : Lind, Srsieve, PrimeGrid, LLR
Decimal Digits:1683577   (log10 is 1683576.78444055)
Rank (*):58 (digit rank is 1)
Entrance Rank (*):57
Currently on list? (*):short
Submitted:9/25/2017 09:34:40 CDT
Last modified:9/26/2017 15:53:59 CDT
Database id:123904
Status Flags:TrialDiv
Score (*):48.2307 (normalized score 89.1124)

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.

James Breslin writes (26 Sep 2017): 
cllr64.3.8.20 -t4 -d -q"301562*5^2408646-1"
Base prime factor(s) taken : 5
Starting N+1 prime test of 301562*5^2408646-1 Using zero-padded FMA3 FFT
length 640K, Pass1=320, Pass2=2K, 4 threads, a = 3
301562*5^2408646-1 may be prime. Starting Lucas sequence...
Using zero-padded FMA3 FFT length 640K, Pass1=320, Pass2=2K, 4 threads, P = 9
301562*5^2408646-1 may be prime, trying to compute gcd's
301562*5^2408646-1 may be prime, but N divides U((N+1)/5), P = 9 Restarting Lucas sequence with P = 11 Using zero-padded FMA3 FFT length 640K, Pass1=320, Pass2=2K, 4 threads, P = 11
301562*5^2408646-1 may be prime, trying to compute gcd's
U((N+1)/5) is coprime to N!
301562*5^2408646-1 is prime! (1683577 decimal digits, P = 11) Time : 31238.467 sec.

PrimeGrid writes (29 Sep 2017): 
For more details, please see the official announcement.

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.
fieldvalue
prime_id123904
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tp -q"301562*5^2408646-1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 301562*5^2408646-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 11, base 8+sqrt(11)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


301562*5^2408646-1 is prime! (108776.9388s+0.0606s)
[Elapsed time: 30.22 hours]
modified2017-09-26 15:53:59
created2017-09-25 09:41:01
id169565

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.