13 267 Exponent Status

PrimeNet Exponent Status

M_n

Details

Composite, with 3 known prime factors. Cofactor is composite.

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Factored

Factor	Digits	Bits	Date
82711943458049277218297229399631	32	106.0	old
2768010176026958221972156342523208826711	40	131.0	2023-06-02 20:20:49
5082562296856722014380488856741826365884196641457	49	161.8	2025-08-08 13:37:03

P-1 factors

Date	Factors	B1	B2
2023-10-10	No new factors discovered	100000000000	122154521813133808

ECM

Digits	B1	Curves
25	50000	280 / 280
30	250000	640 / 640
35	1000000	1566 / 1566
40	3000000	4588 / 4588
45	11000000	1558 / 9201

Estimated T-Level: 40.8 ⓘ

TF below 2^131 is very unlikely to find new factors due to ECM effort.

PRP Cofactor

Status	Proof	Date	User	Residue	Number of known factors	Shift	Type	Base
Factored	No proof (small exponent)	2017-09-21	Oliver Kruse	55D865037FFC6B86	1	0	1	3
Factored	No proof (small exponent)	2017-10-12	kkmrkkblmbrbk	55D865037FFC6B86	1	5567	1	3
Factored	No proof (small exponent)	2020-04-17	Oliver Kruse	F4FE4AAD2461B383	1	5452	5	3
Factored	No proof (small exponent)	2023-06-02	Denial140	F4FE4AAD2461B383	2	7977	5	3
Verified	No proof (small exponent)	2025-08-20	Adel El-Atawy	F4FE4AAD2461B383	3	5239	5	3

History

Date	User	Type	Result
2025-08-20	Adel El-Atawy	C-PRP	M13267/82711943458049277218297229399631/2768010176026958221972156342523208826711/5082562296856722014380488856741826365884196641457 : F4FE4AAD2461B383
2025-08-08	Ryan Propper	F-ECM	Factor: 5082562296856722014380488856741826365884196641457
2025-02-27	masser	NF-PP1	Start=138/53, B1=430000000, B2=429570000000
2025-02-01	masser	NF-PP1	Start=2/7, B1=430000000, B2=429570000000
2025-01-30	masser	NF-PP1	Start=6/5, B1=430000000, B2=429570000000
2023-10-10	-anonymous-	F-PM1	Factor: 82711943458049277218297229399631 / B1=100000000000, B2=122154521813133810
2023-06-02	Denial140	C-PRP	M13267/82711943458049277218297229399631/2768010176026958221972156342523208826711 : F4FE4AAD2461B383
2023-06-02	Denial140	F-ECM	Factor: 2768010176026958221972156342523208826711 / ECM curve 159, B1=3000000, B2=22972799850, Montgomery Sigma=5285225717240609
2023-05-18	JacobZ	NF-PM1	B1=8300000000, B2=34023579430740900
2020-04-17	Oliver Kruse	C-PRP	M13267/82711943458049277218297229399631 : F4FE4AAD2461B383
2017-10-12	kkmrkkblmbrbk	C-PRP	M13267/82711943458049277218297229399631 : 55D865037FFC6B86
2017-09-21	Oliver Kruse	C-PRP	M13267/82711943458049277218297229399631 : 55D865037FFC6B86
2017-09-21	Oliver Kruse	C-PRP	M13267/82711943458049277218297229399631 : 55D865037FFC6B86
2003-09-29	-anonymous-	NF-PM1	B1=16777216, B2=1677721600, E=12
2003-09-29	-anonymous-	NF-PM1	B1=8388608, B2=838860800, 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
2002-08-24	-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
2001-09-30	-anonymous-	NF-PM1	B1=43000000, B2=4290000000
2001-07-17	Alex Kruppa	NF-PM1	B1=1000000, B2=100000000
2001-04-29	-anonymous-	NF-PM1	B1=100000, B2=10000000
2000-09-08	-anonymous-	NF	no factor TF: 1-56
2000-01-25	-anonymous-	NF	no factor TF: 53-54
1999-09-14	-anonymous-	NF	no factor TF: 52-53

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