M4447 Mersenne number exponent details

is 2 ⁴⁴⁴⁷ - 1

has 1339 decimal digits

takes 0.000 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	6,681.7894	80.5970%	200000000	2000000000	0.0263	9.4469%	6,681.8157	82.4300%	14.9300%
PrimeNet	2⁴⁰	0.0000	67.5000%	500	10000	0.0000	2.4592%	0.0000	68.2992%	0.7992%
GPU72	2⁴⁴	0.0005	70.4545%	500	10000	0.0000	0.9818%	0.0005	70.7446%	0.2901%
Difference	+23	+6,681.7889	+10.1425%	+199999500	+1999990000	+0.0263	+8.4651%	+6,681.8152	+11.6854%	+11.6854%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4447	71153	5	16.119	8 2³	-	8	8	1.967e-12	7.050e-10	1.435e-9
4447	155573849	9	27.213	17492 2² × 4373	-	4	4373	7.182e-9	2.133e-8	3.925e-8
4447	78133185209	11	36.185	8784932 2² × 13 × 241 × 701	-	241	701	3.089e-6	2.345e-8	4.322e-8
4447	410532670497221973550121	24	78.442	46158384359930511980 2² × 5 × 73² × 151729 × 2854343839	-	151729	2854343839	14,004,168	0.0137	0.0256
4447	59822255049724275637564293003309197626152000181269 7	51	168.677	67261361647992214568882722063536313948900382484 2² × 3 × 7 × 3643 × 13249 × 9503429681 × 1745676365164420514732374003	2020-09-30	9503429681	1745676365164420514732374003	3.307e+13	8.382e+15	1.565e+16

exponent	prime factors	composite factor	digits	bits*
4447	71153 155573849	11069546077897	14	43.332
4447	71153 78133185209	5559410527175977	16	52.304
4447	155573849 78133185209	12155480357593999441	20	63.398
4447	71153 155573849 78133185209	864898893883885842225473	24	79.517
4447	71153 410532670497221973550121	29210631103888835084011759513	29	94.560
4447	155573849 410532670497221973550121	63868147689501566232568518385729	32	105.655
4447	78133185209 410532670497221973550121	32076225178304814579376103337360289	35	114.627
4447	71153 155573849 410532670497221973550121	4544410312551104942145947788699775537	37	121.774
4447	71153 78133185209 410532670497221973550121	2282319650111922471766347880763196643217	40	130.746
4447	155573849 78133185209 410532670497221973550121	4990221812379591299344856414814885659482361	43	141.840
4447	71153 155573849 78133185209 410532670497221973550121	355069252616245059722284568483323559329148432233	48	157.959
4447	71153 59822255049724275637564293003309197626152000181269 7	42565329135530313844396121400644593386935932688978 829641	56	184.796
4447	155573849 59822255049724275637564293003309197626152000181269 7	93067784739452919496728060474885816118021297272488 249360753	59	195.890
4447	78133185209 59822255049724275637564293003309197626152000181269 7	46741033334201423327731774628727003880173173721489 470428798673	62	204.862
4447	71153 155573849 59822255049724275637564293003309197626152000181269 7	66220520875662935809506916869695504742455693648293 56406765658209	64	212.009
4447	71153 78133185209 59822255049724275637564293003309197626152000181269 7	33257647448284338740380989601578125070859618298051 40289420311979969	67	220.981
4447	155573849 78133185209 59822255049724275637564293003309197626152000181269 7	72716824620390187683736206185916059638764754223977 70927579890004702377	70	232.075
4447	410532670497221973550121 59822255049724275637564293003309197626152000181269 7	24558990120729229359347817712025762656489843664252 8069664226423708383686337	75	247.119
4447	71153 155573849 78133185209 59822255049724275637564293003309197626152000181269 7	51740202222146230242608822787464853914770285572986 8594810091913504588230681	75	248.194
4447	71153 410532670497221973550121 59822255049724275637564293003309197626152000181269 7	17474458240602468566056752736637690902972218462425 799740818702726122624433936561	80	263.238
4447	155573849 410532670497221973550121 59822255049724275637564293003309197626152000181269 7	38207366206348208982375441312102214836305898082560 728888203842343818103652255801113	83	274.332
4447	78133185209 410532670497221973550121 59822255049724275637564293003309197626152000181269 7	19188721236489381476737634567436795402189968008465 197793056257605318851170602983789433	86	283.304
4447	71153 155573849 410532670497221973550121 59822255049724275637564293003309197626152000181269 7	27185687276802941137229597756800088922476735662684 43542582367994289689529168957016593289	88	290.451
4447	71153 78133185209 410532670497221973550121 59822255049724275637564293003309197626152000181269 7	13653350821399289602143129123768303032520227937063 24218569331897391252217341914105569526249	91	299.423
4447	155573849 78133185209 410532670497221973550121 59822255049724275637564293003309197626152000181269 7	29852632201486923239653777728115923249441963522637 95403212067469194976548868861839006697337617	94	310.517
4447	71153 155573849 78133185209 410532670497221973550121 59822255049724275637564293003309197626152000181269 7	21241043390323990492710852466886322869675440305262 5834324748236635630166381666126430843535663462401	99	326.636

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
unknown			200000000	2000000000		-		-	-	0.026	-	-	9.447%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-10-25T00:00:00	Carsten Kossendey	v4_computers	?	?	71153 155573849 78133185209	79.517	24	10,059,193	6.30235e-7	23,455,993
2006-12-18T00:00:00	Hoca	v4_computers	?	?	71153 155573849 78133185209	79.517	24	10,059,193	6.30235e-7	23,455,993

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.529 GHz-days
Estimated T-Level:	33.481

Digits	B1	Curves	Complete	FacMiss
20	11000	1204 / 100	12.040	0.001%
25	50000	1204 / 280	4.300	1.346%
30	250000	1204 / 640	1.881	15.218%
35	1000000	1100 / 1580	0.696	49.836%
40	3000000	1100 / 4700	0.234	79.131%
45	11000000	315 / 9700	0.032	96.805%
50	44000000	201 / 17100	0.012	98.831%

New Calculation Method

Total ECM effort:	20.529 GHz-days
Estimated T-Level:	33.481

Digits	B1	Complete	FacMiss
20	11000	263.067	0.000%
25	50000	74.344	0.000%
30	250000	17.149	0.000%
35	1000000	3.411	3.301%
40	3000000	0.597	55.058%
45	11000000	0.096	90.886%
50	44000000	0.014	98.606%
55	110000000	0.002	99.807%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		785	2.986
11000000	11000000		104	0.984
11000000	1100000000		114	1.590
44000000	4400000000		200	11.16
110000000	900514153782	59822255049724275637564293003309197626152000181269 7	1	3.809

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-28T20:08:00	unconnected	Manual testing	44000000	4400000000						200	11.16
2009-10-13T13:59:00	Carsten Kossendey	durandal	3000000	300000000						1	0.004
2010-03-24T21:44:00	James Hintz	NEW_OMFG	3000000	300000000						100	0.380
2010-07-02T02:53:00	James Hintz	NEW_OMFG	3000000	300000000						684	2.602
2011-01-02T11:11:00	James Hintz	OMFG	11000000	1100000000						3	0.042
2011-02-05T19:39:00	James Hintz	OMFG	11000000	1100000000						11	0.153
2016-10-04T23:53:07	kkmrkkblmbrbk	kel1	11000000	11000000						104	0.984
2020-05-15T20:51:57	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.395
2020-09-30T23:26:32	Ryan Propper	Manual testing	110000000	900514153782	59822255049724275637564293003309197626152000181269 7	168.677	1	2	15305037124375852950	1	3.809

Lucas-Lehmer results:
Exponent "4447" not found

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T18:34:37

Oliver Kruse

Oliver-PC

3352014D5A7D50__

2017-09-21T19:21:12

Oliver Kruse

Manual testing

3352014D5A7D50__

2017-10-02T09:55:58

kkmrkkblmbrbk

Manual testing

71153

155573849

78133185209

410532670497221973550121

3352014D5A7D50__

2017-12-07T02:54:17

ATH

Manual testing

71153

155573849

78133185209

410532670497221973550121

3352014D5A7D50__

2020-04-17T12:32:27

Oliver Kruse

IOS-1

71153

155573849

78133185209

410532670497221973550121

16CC0441581578__

2020-09-30T23:36:27

M Miller

cruncher

71153

155573849

78133185209

410532670497221973550121

59822255049724275637564293003309197626152000181269
7

16CC04415815786C

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 200000000, B2 = 2000000000 (P-1 stage 2)

B1 = 200000000 (P-1 stage 1)

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TF factor-bounds graph:

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2¹⁷⁰

Last modified: 2020-09-30T23:36:27+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront