8508301 · 217016603 - 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:8508301 · 217016603 - 1
Verification status (*):Proven
Official Comment:Woodall
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):L4784 : Bertolotti, Gcwsieve, MultiSieve, PrimeGrid, LLR
Decimal Digits:5122515   (log10 is 5122514.85714854)
Rank (*):16 (digit rank is 1)
Entrance Rank (*):16
Currently on list? (*):short
Submitted:3/22/2018 05:20:51 CDT
Last modified:4/3/2018 03:48:20 CDT
Database id:124539
Status Flags:TrialDiv
Score (*):51.6396 (normalized score 2313.5)

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.
Woodall Primes (archivable *)
Prime on list: yes, rank 1
Subcategory: "Woodall Primes"
(archival tag id 219090, tag last modified 2018-03-28 13:50:05)

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 (28 Mar 2018): 
C:test>cllr64 -v LLR Program - Version 3.8.20, using Gwnum Library Version 28.13
C:test>cllr64 -d -t4 -q"17016602*2^17016602-1"
Starting Lucas Lehmer Riesel prime test of 17016602*2^17016602-1
Using zero-padded FMA3 FFT length 1792K, Pass1=448, Pass2=4K, 4 threads
V1 = 4 ; Computing U0...done.
17016602*2^17016602-1 is prime! (5122515 decimal digits) Time : 31478.216 sec.

PrimeGrid writes (1 Apr 2018): 
For more information, 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_id124539
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tp -q"8508301*2^17016603-1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 8508301*2^17016603-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


8508301*2^17016603-1 is prime! (1031118.3994s+0.0023s)
[Elapsed time: 11.93 days]
modified2018-09-25 13:41:13
created2018-03-22 05:23:02
id170204

Query times: 0.0005 seconds to select prime, 0.0009 seconds to seek comments.