109 357 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
21377685210103128740719	23	74.2	2008-01-13 02:15:49
652851013404912882650969569799279	33	109.0	2018-10-09 20:16:16
368879136944143086375941914092497977	36	118.2	2024-09-16 16:49:51

ECM

Digits	B1	Curves
25	50000	280 / 280
30	250000	640 / 640
35	1000000	679 / 1566

Estimated T-Level: 32.2 ⓘ

TF below 2^102 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	D1AEAA3A63E4C03B	1	0	1	3
Factored	No proof (small exponent)	2017-10-13	kkmrkkblmbrbk	D1AEAA3A63E4C03B	1	44211	1	3
Factored	No proof (small exponent)	2018-10-11	Oliver Kruse	D07FA48F75ED9C6B	2	76302	5	3
Factored	No proof (small exponent)	2018-10-14	Chang Chia-Tche	D07FA48F75ED9C6B	2	87160	5	3
Factored	Not Uploaded	2022-04-15	LordJulius	D07FA48F75ED9C6B	2	12137	5	3
Factored	Certified Good	2022-11-11	LordJulius	D07FA48F75ED9C6B	2	34559	5	3
Verified	Certified Good	2024-09-16	cramsey87	D07FA48F75ED9C6B	3	18772	5	3

History

Date	User	Type	Result
2026-02-10	Jason Lynch	NF-PM1	B1=896551000, B2=137382320995920
2025-12-16	ViliamF	NF-PM1	B1=100000000, B2=2943700209450
2024-09-17	yakman	CERT	Proof certified good
2024-09-16	cramsey87	C-PRP	M109357/21377685210103128740719/652851013404912882650969569799279/368879136944143086375941914092497977 : D07FA48F75ED9C6B Proof Certified Good Proof Power: 5
2024-09-16	cramsey87	F-ECM	Factor: 368879136944143086375941914092497977 / ECM curve 31, B1=1130227, B2=5789138355, Edwards Sigma=6650176007207440
2022-11-11	Jim Donovan	CERT	Proof certified good
2022-11-11	LordJulius	C-PRP	M109357/21377685210103128740719/652851013404912882650969569799279 : D07FA48F75ED9C6B Proof Not Uploaded Proof Power: 5
2022-05-07	LordJulius	NF	no factor TF: 62-63
2022-05-07	LordJulius	NF	no factor TF: 60-61
2022-05-07	LordJulius	NF	no factor TF: 61-62
2022-05-07	LordJulius	NF	no factor TF: 59-60
2022-05-07	LordJulius	NF	no factor TF: 57-58
2022-05-07	LordJulius	NF	no factor TF: 58-59
2022-05-07	LordJulius	NF	no factor TF: 1-57
2022-04-15	LordJulius	C-PRP	M109357/21377685210103128740719/652851013404912882650969569799279 : D07FA48F75ED9C6B Proof Not Uploaded Proof Power: 5
2018-10-26	J.R. Allen	NF	no factor TF: 1-57
2018-10-14	Chang Chia-Tche	C-PRP	M109357/21377685210103128740719/652851013404912882650969569799279 : D07FA48F75ED9C6B
2018-10-11	Oliver Kruse	C-PRP	M109357/21377685210103128740719/652851013404912882650969569799279 : D07FA48F75ED9C6B
2018-10-09	Niels_Mache_Nextcloud	F-ECM	Factor: 652851013404912882650969569799279
2017-10-13	kkmrkkblmbrbk	C-PRP	M109357/21377685210103128740719 : D1AEAA3A63E4C03B
2017-09-21	Oliver Kruse	C-PRP	M109357/21377685210103128740719 : D1AEAA3A63E4C03B
2017-09-21	Oliver Kruse	C-PRP	M109357/21377685210103128740719 : D1AEAA3A63E4C03B
2016-12-10	kkmrkkblmbrbk	NF-PM1	B1=100000000, B2=2000000000, E=12
2008-01-13	James Heinrich	F-ECM	Factor: 21377685210103128740719
2006-02-01	Joss	NF-PM1	B1=2000000
2003-09-29	-anonymous-	NF-PM1	B1=262144, B2=26214400, E=12
2003-02-02	-anonymous-	NF-PM1	B1=131072, B2=13107200, E=30
2002-07-20	-anonymous-	NF-PM1	B1=65536, B2=6553600, E=12
2002-06-02	-anonymous-	NF-PM1	B1=32768, B2=3276800
2002-05-05	-anonymous-	NF	no factor TF: 1-57
2001-01-08	-anonymous-	NF-PM1	B1=1000000, B2=25000000
2000-12-14	-anonymous-	NF	no factor TF: 1-56
2000-04-12	-anonymous-	NF	no factor TF: 1-54
1999-09-14	-anonymous-	NF	no factor TF: 52-53

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