16 553 Exponent Status

PrimeNet Exponent Status

M_n

Details

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

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Factored

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

P-1 factors

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

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	Software
Factored		Unknown	6AAA	0	Unknown,(aka U)
Factored		George Woltman	5396FD0D8AFC6AAA	0	Woltman,Prime95,first web release,(aka W4)
Factored		Brian J. Beesley	5396FD0D8AFC6AAA	0	Mac,John Sweeney,v1.4,(aka J3)
Factored	2015-04-11	MadPoo 🙂	5396FD0D8AFC6AAA	6569	Windows 64-bit,Prime95,v26,(aka We4)

PRP Cofactor

Status	Proof	Date	User	Residue	Number of known factors	Shift	Type	Base
Verified	No proof (small exponent)	2023-10-19	Anton Repko	31B6D035ECC70A22	1	5290	5	3
Verified	No proof (small exponent)	2023-10-20	Naegi Makoto	31B6D035ECC70A22	1	1229	5	3

History

Date	User	Type	Result
2023-10-20	Naegi Makoto	C-PRP	M16553/1850475917485872002512582039081380045643275936063486278441 : 31B6D035ECC70A22
2023-10-19	Anton Repko	C-PRP	M16553/1850475917485872002512582039081380045643275936063486278441 : 31B6D035ECC70A22
2023-10-19	Anton Repko	F-PM1	Factor: 1850475917485872002512582039081380045643275936063486278441 / 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 TF: 65-66
2021-05-10	ATH	NF-PP1	Start=2/7, B1=1000000000, B2=241000000000
2021-02-11	Ruslan Borisov	NF	no factor TF: 64-65
2018-10-30	snme2pm1	NF	no factor TF: 63-64
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 TF: 62-63
2016-06-08	Sid & Andy	NF	no factor TF: 62-63
2016-05-03	Joss	NF-PM1	B1=992344772, B2=49617238600, E=12
2016-02-23	LaurV	NF	no factor TF: 57-58
2016-02-23	LaurV	NF	no factor TF: 58-59
2016-02-23	LaurV	NF	no factor TF: 59-60
2015-08-28	snme2pm1	NF	no factor TF: 61-62
2015-04-11	MadPoo 🙂	C-LL	5396FD0D8AFC6AAA
2012-12-25	bcp19	NF	no factor TF: 60-61
2012-10-12	Joss	NF-PM1	B1=496172386, B2=49617238600, E=12
2010-03-17	GrunwalderGIMP	NF	no factor TF: 1-60
2003-09-29	-anonymous-	NF-PM1	B1=8388608, B2=838860800, E=12
2003-09-29	-anonymous-	NF-PM1	B1=16777216, B2=1677721600, E=12
2003-07-06	-anonymous-	NF-PM1	B1=4194304, B2=419430400, E=12
2003-05-19	-anonymous-	NF-PM1	B1=2097152, B2=209715200, E=12
2003-04-27	-anonymous-	NF-PM1	B1=1048576, B2=104857600, E=48
2003-04-03	-anonymous-	NF-PM1	B1=524288, B2=52428800, E=48
2003-03-27	-anonymous-	NF-PM1	B1=262144, B2=26214400, E=30
2003-02-02	-anonymous-	NF-PM1	B1=131072, B2=13107200, E=30
2002-10-12	-anonymous-	NF	no factor TF: 1-57
2002-07-14	-anonymous-	NF-PM1	B1=65536, B2=6553600, E=12
2002-06-09	-anonymous-	NF-PM1	B1=32768, B2=3276800
2002-04-28	-anonymous-	NF-PM1	B1=16384, B2=1638400
2001-08-18	Alex Kruppa	NF-PM1	B1=1000000, B2=100000000
2001-07-29	Alex Kruppa	NF-PM1	B1=1000000, B2=100000000
2001-04-29	-anonymous-	NF-PM1	B1=100000, B2=10000000
2000-09-23	-anonymous-	NF	no factor TF: 1-56
2000-03-08	-anonymous-	NF	no factor TF: 53-54
1999-09-22	-anonymous-	NF	no factor TF: 52-53

Username
Password