12 821 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
1740358863860866135847769457645783	34	110.4	old

P-1 factors

Date	Factors	B1	B2
2024-09-25	No new factors discovered	500000000000	707246050405794944

ECM

Digits	B1	Curves
25	50000	280 / 280
30	250000	640 / 640
35	1000000	1566 / 1566
40	3000000	4588 / 4588
45	11000000	3347 / 9201

Estimated T-Level: 41.8 ⓘ

TF below 2^134 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
Verified	No proof (small exponent)	2017-09-21	Oliver Kruse	DA8FA054BA0E432A	1	0	1	3
Verified	No proof (small exponent)	2017-10-12	kkmrkkblmbrbk	DA8FA054BA0E432A	1	3970	1	3
Verified	No proof (small exponent)	2020-04-17	Oliver Kruse	E65AA21CD688C269	1	7102	5	3
Verified	No proof (small exponent)	2024-07-01	kkmrkkblmbrbk	E65AA21CD688C269	1	4159	5	3

History

Date	User	Type	Result
2025-03-09	masser	NF-PP1	Start=95/61, B1=430000000, B2=429570000000
2025-02-19	masser	NF-PP1	Start=6/5, B1=430000000, B2=429570000000
2025-01-17	masser	NF-PP1	Start=2/7, B1=430000000, B2=429570000000
2024-09-25	Anton Repko	F-PM1	Factor: 1740358863860866135847769457645783 / B1=500000000000, B2=707246050405794900
2024-07-01	kkmrkkblmbrbk	C-PRP	M12821/1740358863860866135847769457645783 : E65AA21CD688C269
2023-05-15	JacobZ	NF-PM1	B1=8600000000, B2=36024966470342850
2020-04-17	Oliver Kruse	C-PRP	M12821/1740358863860866135847769457645783 : E65AA21CD688C269
2017-10-12	kkmrkkblmbrbk	C-PRP	M12821/1740358863860866135847769457645783 : DA8FA054BA0E432A
2017-09-21	Oliver Kruse	C-PRP	M12821/1740358863860866135847769457645783 : DA8FA054BA0E432A
2017-09-21	Oliver Kruse	C-PRP	M12821/1740358863860866135847769457645783 : DA8FA054BA0E432A
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
2002-08-17	-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
2000-07-25	-anonymous-	NF	no factor TF: 1-55
2000-01-19	-anonymous-	NF	no factor TF: 53-54
1999-09-14	-anonymous-	NF	no factor TF: 52-53

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