10999999 - 1022306 · 10287000 - 1

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Description:10999999 - 1022306 · 10287000 - 1
Verification status (*):PRP
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH13 : Propper, Batalov, EMsieve, OpenPFGW, CHG
Decimal Digits:999999   (log10 is 999999)
Rank (*):1159 (digit rank is 1)
Entrance Rank (*):1113
Currently on list? (*):short
Submitted:9/10/2021 17:12:17 CDT
Last modified:9/12/2021 08:37:16 CDT
Database id:132705
Status Flags:Verify, TrialDiv
Score (*):46.633 (normalized score 8.816)

User comments about this prime (disclaimer):

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Serge Batalov writes (12 Sep 2021):  (report abuse)
Currently, the largest known proven under-one-million-decimal digit prime. CHG proof is available at dropbox
See also its sibling - the smallest known proven one-million-decimal digit prime.

Also, a nearly repdigit prime (only 5 digits are different from the rest which are 999994 nines).

CHG proof certificate (large) will be available on dropbox (arranging data transfer now)

Prerequsite of CHG is small:
Running N+1 test using discriminant 3, base 1+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 336K, Pass1=448, Pass2=768, clm=4, 16 threads on A 3321925-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 28.70%
10^999999-1022306*10^287000-1 is Lucas PRP! (37368.5112s+0.0668s)

(CHG log) 
n=10^999999-1022306*10^287000-1;
F=10^287000*2*11*1123*1289*1439*53101;
G=1;

Target "MS" has 999999 digits.
Modulus provides 28.701567323452141644%.
Right endpoint has 138953 digits.

LLL[1, 1] for client 1 has [h, u] = [4, 1] and digits in [1, 11727]
LLL[2, 1] for client 2 has [h, u] = [4, 1] and digits in [11727, 32495]
LLL[3, 1] for client 3 has [h, u] = [5, 1] and digits in [32495, 59755]
LLL[4, 1] for client 4 has [h, u] = [5, 1] and digits in [59755, 73385]
LLL[5, 1] for client 5 has [h, u] = [5, 1] and digits in [73385, 80200]
LLL[6, 1] for client 6 has [h, u] = [6, 2] and digits in [80200, 93773]
LLL[7, 1] for client 7 has [h, u] = [6, 2] and digits in [93773, 104630]
LLL[8, 1] for client 8 has [h, u] = [6, 2] and digits in [104630, 113317]
LLL[9, 1] for client 9 has [h, u] = [6, 2] and digits in [113317, 120266]
LLL[10, 1] for client 10 has [h, u] = [6, 2] and digits in [120266, 125825]
LLL[11, 1] for client 11 has [h, u] = [6, 2] and digits in [125825, 130272]
LLL[12, 1] for client 12 has [h, u] = [6, 2] and digits in [130272, 133830]
LLL[13, 1] for client 13 has [h, u] = [6, 2] and digits in [133830, 136676]
LLL[14, 1] for client 14 has [h, u] = [6, 2] and digits in [136676, 138953]

LLL was split between 14 clients.
...
Validated in 28 sec.

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_id132705
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tp -q"10^999999-1022306*10^287000-1" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 10^999999-1022306*10^287000-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 28.70%


10^999999-1022306*10^287000-1 is Lucas PRP! (139715.6995s+0.0109s)
[Elapsed time: 1.62 days]
modified2021-09-12 08:09:37
created2021-09-10 17:21:01
id178418

Query times: 0.0006 seconds to select prime, 0.001 seconds to seek comments.
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