10999999 + 308267 · 10292000 + 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 PrimePages database: 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:10999999 + 308267 · 10292000 + 1
Verification status (*):PRP
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH10 : Batalov, OpenPFGW, Primo, CHG
Decimal Digits:1000000   (log10 is 999999)
Rank (*):2664 (digit rank is 22)
Entrance Rank (*):924
Currently on list? (*):short
Submitted:2/19/2021 06:47:24 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:131964
Status Flags:Verify
Score (*):46.633 (normalized score 5.2053)

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.

Serge Batalov writes (23 Feb 2021):  (report abuse)
Currently, the smallest known proven one-million-decimal digit prime. CHG proof is available at dropbox 
(CHG log) 
Target "M1" has 1000000 digits.
Modulus provides 29.201415589110682960%.
Right endpoint has 123958 digits.

LLL[1, 1] for client 1 has [h, u] = [5, 1] and digits in [1, 11327]
LLL[2, 1] for client 2 has [h, u] = [5, 1] and digits in [11327, 51670]
LLL[3, 1] for client 3 has [h, u] = [5, 1] and digits in [51670, 71842]
LLL[4, 1] for client 4 has [h, u] = [5, 1] and digits in [71842, 81928]
LLL[5, 1] for client 5 has [h, u] = [6, 2] and digits in [81928, 99154]
LLL[6, 1] for client 6 has [h, u] = [6, 2] and digits in [99154, 112934]
LLL[7, 1] for client 7 has [h, u] = [6, 2] and digits in [112934, 123958]

LLL was split between 7 clients.
...
Testing a PRP called "M1".

Pol[1, 1] with [h, u]=[4, 1] has ratio=2.7362328007716239617 E-168015 at X, ratio=8.371138677385148796 E-179342 at Y, witness=11.
Pol[2, 1] with [h, u]=[4, 1] has ratio=8.371138677385148796 E-179342 at X, ratio=9.047203494429615826 E-188633 at Y, witness=11.
Pol[3, 1] with [h, u]=[4, 1] has ratio=9.047203494429615826 E-188633 at X, ratio=2.5468952372881540576 E-148289 at Y, witness=11.
Pol[4, 1] with [h, u]=[4, 1] has ratio=2.5468952372881540576 E-148289 at X, ratio=1.3513238520681594830 E-128117 at Y, witness=11.
Pol[5, 1] with [h, u]=[5, 2] has ratio=1.5108259964206371894 E-128117 at X, ratio=1.3450299833181739897 E-93666 at Y, witness=3.
Pol[6, 1] with [h, u]=[6, 2] has ratio=4.072195893759488275 E-74335 at X, ratio=1.5753138472238822219 E-77157 at Y, witness=13.
Pol[7, 1] with [h, u]=[6, 2] has ratio=1.5753138472238822219 E-77157 at X, ratio=1.2850023045853379356 E-44084 at Y, witness=13.

Validated in 12 sec.

n=10^999999+308267*10^292000+1;
F=10^292000*837*87327593609;
G=1;

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_id131964
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"10^999999+308267*10^292000+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 10^999999+308267*10^292000+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N-1 test using base 23 Calling Brillhart-Lehmer-Selfridge with factored part 29.20% 10^999999+308267*10^292000+1 is PRP! (52689.1754s+0.0313s) [Elapsed time: 14.64 hours]
modified2021-04-20 22:39:25
created2021-02-19 06:51:01
id177663

Query times: 0.0002 seconds to select prime, 0.0006 seconds to seek comments.
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