16 553 Exponent Status

PrimeNet Exponent Status

M_n

Status

Details

Composite, with 1 known prime factor. Cofactor is composite.

Factored

Factor	Digits	Bits	Date
1850475917485872002512582039081380045643275936063486278441	58	190.2	2023-10-19 14:31:45

ECM

Digits	B1	Curves
25	50000	280 / 280
30	250000	640 / 640
35	1000000	1566 / 1566
40	3000000	4588 / 4588
45	11000000	9201 / 9201
50	44000000	16550 / 16550
55	110000000	10126 / 40830

Estimated T-Level: 51.2 ⓘ

TF below 2^165 is very unlikely to find new factors due to ECM effort.

Status	Date	User	Residue	Shift
Verified (Factored)		Unknown	6AAA	0
Verified (Factored)		George Woltman	5396FD0D8AFC6AAA	0
Verified (Factored)		Brian J. Beesley	5396FD0D8AFC6AAA	0
Verified (Factored)	2015-04-11	MadPoo	5396FD0D8AFC6AAA	6569

PRP Cofactor

Status	Date	User	Residue	Number of known factors	Shift	Type	Base
Verified	2023-10-19	Anton Repko	31B6D035ECC70A22	1	5290	5	3
Verified	2023-10-20	Naegi Makoto	31B6D035ECC70A22	1	1229	5	3

P-1 factors

Date	Factor	B1	B2
2023-10-19	1850475917485872002512582039081380045643275936063486278441	1000000000000	1402034650733707008

History

Date	User	Type	Result
2023-10-20	Naegi Makoto	C-PRP	M16553/1850475917485872002512582039081380045643275936063486278441 : 31B6D035ECC70A22 PRP: Verified PRP without proof (small exponent)
2023-10-19	Anton Repko	C-PRP	M16553/1850475917485872002512582039081380045643275936063486278441 : 31B6D035ECC70A22 PRP: Verified PRP without proof (small exponent)
2023-10-19	Anton Repko	F-PM1	Factor: 1850475917485872002512582039081380045643275936063486278441 / (P-1, B1=1000000000000, B2=1402034650733706990)
2023-08-26	masser	NF-PP1	Start=6/5, B1=460000000, B2=82340000000
2023-07-08	masser	NF-PP1	Start=187/61, B1=460000000, B2=18400000000
2022-04-23	-Anonymous-	NF-PM1	B1=100000000000, B2=100609955472526500
2022-01-16	Ruslan Borisov	NF	no factor from 2^65 to 2^66
2021-05-10	ATH	NF-PP1	Start=2/7, B1=1000000000, B2=241000000000
2021-02-11	Ruslan Borisov	NF	no factor from 2^64 to 2^65
2018-10-30	snme2pm1	NF	no factor from 2^63 to 2^64
2016-09-16	BloodIce	NF-PM1	B1=100000000000, B2=5000000000000, E=12
2016-09-07	BloodIce	NF-PM1	B1=100000000000
2016-08-23	BloodIce	NF-PM1	B1=50000000000
2016-06-19	Sid & Andy	NF	no factor from 2^62 to 2^63
2016-06-08	Sid & Andy	NF	no factor from 2^62 to 2^63
2016-05-03	Joss	NF-PM1	B1=992344772, B2=49617238600, E=12
2016-02-23	LaurV	NF	no factor from 2^57 to 2^58
2016-02-23	LaurV	NF	no factor from 2^58 to 2^59
2016-02-23	LaurV	NF	no factor from 2^59 to 2^60
2015-08-28	snme2pm1	NF	no factor from 2^61 to 2^62
2015-04-11	MadPoo	C-LL	5396FD0D8AFC6AAA
2012-12-25	bcp19	NF	no factor from 2^60 to 2^61
2012-10-12	Joss	NF-PM1	B1=496172386, B2=49617238600, E=12
2010-03-17	GrunwalderGIMP	NF	no factor from 2^1 to 2^60

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