M28 411 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	1,045.8596	77.6119%	3000000000	925584566816910	40,279.8493	31.8830%	41,325.7089	84.7499%
Target	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7307%	0.0001	66.4991%
Difference	+23	+1,045.8595	+11.7028%	+2999999500	+925584566806910	+40,279.8493	+30.1523%	+41,325.7089	+18.2508%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
28411	3409321	7	21.701	60 2² × 3 × 5	-	4	5	9.961e-12	3.238e-9	6.502e-9
28411	20910497	8	24.318	368 2⁴ × 23	2008-08-26	16	23	8.493e-11	1.308e-8	2.601e-8
28411	177739217	9	27.405	3128 2³ × 17 × 23	2008-08-26	17	23	1.055e-9	1.384e-8	2.763e-8
28411	375536599	9	28.484	6609 3 × 2203	2008-08-26	3	2203	1.801e-9	9.813e-8	1.789e-7
28411	145954745454377	15	47.053	2568630908 2² × 2531 × 253717	2008-08-26	2531	253717	0.0011	1.295e-5	2.062e-5
28411	259400137814578063	18	57.848	4565135648421 3² × 23 × 113 × 195166331	2009-04-04	113	195166331	0.8280	0.0085	0.0159
28411	73527519400535957290573035651975101657	38	125.790	1293997384825172596715586140086148 2² × 7 × 19 × 24851 × 127217 × 3013099 × 255340289072333	2023-02-18	3013099	255340289072333	5.080e+12	11,111	20,753

exponent	prime factors	composite factor	digits	bits*
28411	3409321 20910497	71290596542537	14	46.019
28411	3409321 177739217	605970045041657	15	49.106
28411	3409321 375536599	1280324813239279	16	50.185
28411	20910497 177739217	3716615363860849	16	51.723
28411	20910497 375536599	7852656926779703	16	52.802
28411	177739217 375536599	66747581061102983	17	55.890
28411	3409321 145954745454377	497606578727262048017	21	68.754
28411	20910497 145954745454377	3051986266959513895369	22	71.370
28411	3409321 20910497 177739217	12671134808933433573529	23	73.424
28411	177739217 145954745454377	25941882174495277202809	23	74.458
28411	3409321 20910497 375536599	26772228166265503811663	23	74.503
28411	375536599 145954745454377	54811348715847448243823	23	75.537
28411	3409321 177739217 375536599	227563929810820683104543	24	77.591
28411	3409321 259400137814578063	884378337254135096325223	24	79.549
28411	20910497 177739217 375536599	1395725093535450742712551	25	80.207
28411	20910497 259400137814578063	5424185803571321142627311	25	82.166
28411	177739217 259400137814578063	46105577384855196102996671	26	85.253
28411	375536599 259400137814578063	97414245535017938399027737	26	86.332
28411	3409321 20910497 145954745454377	10405200871656676873273334449	29	93.071
28411	3409321 177739217 145954745454377	88444203677032412968357982689	29	96.159
28411	3409321 375536599 145954745454377	186869482215261738094078874183	30	97.238
28411	20910497 177739217 145954745454377	542457649384136970463505986073	30	98.775
28411	20910497 375536599 145954745454377	1146132542888681918960116110031	31	99.855
28411	3409321 20910497 177739217 375536599	4758474871617376461595497087871	31	101.908
28411	177739217 375536599 145954745454377	9742126203468680942305125106591	31	102.942
28411	3409321 20910497 259400137814578063	18492790568017580169303286565831	32	103.867
28411	145954745454377 259400137814578063	37860681085557054887533471531751	32	104.900
28411	3409321 177739217 259400137814578063	157188713195311902033064713370391	33	106.954
28411	3409321 375536599 259400137814578063	332116433001692892760511643336577	33	108.033
28411	20910497 177739217 259400137814578063	964090537589282423546123579955487	33	109.571
28411	20910497 375536599 259400137814578063	2036980289017255995839054297455289	34	110.650
28411	177739217 375536599 259400137814578063	17314331726039834451997423535661929	35	113.738
28411	3409321 20910497 177739217 145954745454377	1849412255655975240277610691944386433	37	120.476
28411	3409321 20910497 375536599 145954745454377	3907533747253783928631022016366998951	37	121.556
28411	3409321 177739217 375536599 145954745454377	33214035450136046778900651433527934711	38	124.643
28411	3409321 145954745454377 259400137814578063	129079215099292463926220502696100851071	39	126.602
28411	20910497 177739217 375536599 145954745454377	203712700751253242438028491625995785727	39	127.260
28411	20910497 145954745454377 259400137814578063	791685658257497539554603993864264690247	39	129.218
28411	3409321 20910497 177739217 259400137814578063	3286894115704429941526693589737420894327	40	131.272
28411	177739217 145954745454377 259400137814578063	6729327811233620944536222291345213378967	40	132.306
28411	3409321 20910497 375536599 259400137814578063	6944719675932600228990000436454563348769	40	132.351
28411	375536599 145954745454377 259400137814578063	14218071410693724412920647397697091054849	41	133.385
28411	3409321 177739217 375536599 259400137814578063	59030114754553854433718308006026463440209	41	135.439
28411	20910497 177739217 375536599 259400137814578063	362051281614360780188988768850188159368713	42	138.055
28411	3409321 73527519400535957290573035651975101657	250678915970154650445853752482027405556344897	45	147.491
28411	3409321 20910497 177739217 375536599 145954745454377	694521988637963455762061735098831578190561367	45	148.961
28411	20910497 73527519400535957290573035651975101657	1537496973842348933316655590281518407273393529	46	150.107
28411	3409321 20910497 145954745454377 259400137814578063	2699110540096109769051842042965308758017592287	46	150.919
28411	177739217 73527519400535957290573035651975101657	13068723726203570429171892838095139072010582569	47	153.195
28411	3409321 177739217 145954745454377 259400137814578063	22942438622722819792247177918551354222393151407	47	154.007
28411	375536599 73527519400535957290573035651975101657	27612274568583792178111052569848477308949044543	47	154.274
28411	3409321 375536599 145954745454377 259400137814578063	48473969439977739209183034506564044172208847529	47	155.086
28411	20910497 177739217 145954745454377 259400137814578063	140713589008817197059861842614507210325249316599	48	156.623
28411	20910497 375536599 145954745454377 259400137814578063	297306939579096892255203958647602829411146849953	48	157.703
28411	3409321 20910497 177739217 375536599 259400137814578063	1234349037484754109474703378405092345687099973873	49	159.756
28411	177739217 375536599 145954745454377 259400137814578063	2527108879786788003966300551599768567266565313233	49	160.790
28411	3409321 20910497 73527519400535957290573035651975101657	52418207203571709076840735537141766178037332996838 09	52	171.808
28411	145954745454377 73527519400535957290573035651975101657	10731690377996992192333804988278638929134003230602 689	53	172.842
28411	3409321 177739217 73527519400535957290573035651975101657	44555474242944082939154746862667357636126191374725 649	53	174.896
28411	3409321 375536599 73527519400535957290573035651975101657	94139107544438662932469751858488380507423465490385 303	53	175.975
28411	20910497 177739217 73527519400535957290573035651975101657	27327350827060858084848757767530989127986007077732 6793	54	177.513
28411	3409321 20910497 177739217 145954745454377 259400137814578063	47973779399312965509732523712433433681328932531661 9279	54	178.324
28411	20910497 375536599 73527519400535957290573035651975101657	57738638452954768058901463042865887522334706906926 7871	54	178.592
28411	3409321 20910497 375536599 145954745454377 259400137814578063	10136147925527461958004042155004039259708405896286 11913	55	179.404
28411	177739217 375536599 73527519400535957290573035651975101657	49077840614090960206281830228107061655348702699709 42831	55	181.679
28411	3409321 177739217 375536599 145954745454377 259400137814578063	86157253731435718644703917628806745715218137202768 44793	55	182.491
28411	259400137814578063 73527519400535957290573035651975101657	19073048665663089525084295508233937231830547440987 150391	56	183.638
28411	20910497 177739217 375536599 145954745454377 259400137814578063	52843102649454991196573315785325305826521812182662 706801	56	185.108
28411	3409321 145954745454377 73527519400535957290573035651975101657	36587777371203083418159680356443117552514069028161 590264169	59	194.543
28411	20910497 145954745454377 73527519400535957290573035651975101657	22440497945403497124681945220598551449173978715150 7836526433	60	197.160
28411	3409321 20910497 177739217 73527519400535957290573035651975101657	93167711049065951746694651680756519384814381636262 6559237553	60	199.214
28411	177739217 145954745454377 73527519400535957290573035651975101657	19074422448716194206205239012473394610899962222827 92380954513	61	200.247
28411	3409321 20910497 375536599 73527519400535957290573035651975101657	19684955258906620279334199488276657051353368528663 05407225591	61	200.293
28411	375536599 145954745454377 73527519400535957290573035651975101657	40301425060740148801385909980273949277959855884755 46547314711	61	201.327
28411	3409321 177739217 375536599 73527519400535957290573035651975101657	16732211264027320654144097571512019554987509443687 604783527751	62	203.380
28411	3409321 259400137814578063 73527519400535957290573035651975101657	65026145349867150042749915446427635117161753832053 752558194511	62	205.339
28411	20910497 177739217 375536599 73527519400535957290573035651975101657	10262420389274271811205755921393420284229840817561 6590154797007	63	205.997
28411	3409321 20910497 177739217 375536599 145954745454377 259400137814578063	18015909956794254004129253354654105698578317123240 7802213492121	63	206.809
28411	20910497 259400137814578063 73527519400535957290573035651975101657	39882692690420203652500658597203921978438096677311 9485289554327	63	207.955
28411	177739217 259400137814578063 73527519400535957290573035651975101657	33900287356378523179893845426301170564127089788424 09817557583847	64	211.043
28411	375536599 259400137814578063 73527519400535957290573035651975101657	71626278284646047200826815234731492844211183302964 67660537660209	64	212.122
28411	3409321 20910497 145954745454377 73527519400535957290573035651975101657	76506860895720996220617774161436274025249278287116 5848734135081993	66	218.861
28411	3409321 177739217 145954745454377 73527519400535957290573035651975101657	65030829017279543947293851675244806188228070105493 92003028221215673	67	221.948
28411	3409321 375536599 145954745454377 73527519400535957290573035651975101657	13740049478950766485168981199985756102628337382487 038830237537821231	68	223.028
28411	20910497 177739217 145954745454377 73527519400535957290573035651975101657	39885565339061263280027203175460788059103982736055 663233572201222961	68	224.565
28411	20910497 375536599 145954745454377 73527519400535957290573035651975101657	84272282782833169929093366648478847555493173259861 150650984622421367	68	225.644
28411	3409321 20910497 177739217 375536599 73527519400535957290573035651975101657	34987885343980949645651818983680937036850765125970 1328763142686702247	69	227.698
28411	177739217 375536599 145954745454377 73527519400535957290573035651975101657	71631437342801314884218201547263771901623001423892 7866966770185721287	69	228.732
28411	3409321 20910497 259400137814578063 73527519400535957290573035651975101657	13597290172599609913674719786927787248345055020198 98496706868647681967	70	229.656
28411	145954745454377 259400137814578063 73527519400535957290573035651975101657	27838019630358011211038470835481566491626451325471 50738188473728211407	70	230.690
28411	3409321 177739217 259400137814578063 73527519400535957290573035651975101657	11557696159013578302619886498264253312886033388455 983481605239318837887	71	232.744
28411	3409321 375536599 259400137814578063 73527519400535957290573035651975101657	24419697470768774628877007854289000791511891566964 683420891916241408089	71	233.823
28411	20910497 177739217 259400137814578063 73527519400535957290573035651975101657	70887185706469103981760071510513434817766781863957 273962808404359941959	71	235.360
28411	20910497 375536599 259400137814578063 73527519400535957290573035651975101657	14977410771922563160547475174854071769243994158230 9296126269762187313873	72	236.440
28411	177739217 375536599 259400137814578063 73527519400535957290573035651975101657	12730798618937091551619999892424846743371198702912 41539849785524559716353	73	239.527
28411	3409321 20910497 177739217 145954745454377 73527519400535957290573035651975101657	13598269550733368518712562435736514940645244952567 2029831145610645666619481	75	246.266
28411	3409321 20910497 375536599 145954745454377 73527519400535957290573035651975101657	28731126340945156573582652587535855302674154095148 3077998565543898237361807	75	247.345
28411	3409321 177739217 375536599 145954745454377 73527519400535957290573035651975101657	24421456359299672166237768311731887008341323283750 75794335015896353483916127	76	250.433
28411	3409321 145954745454377 259400137814578063 73527519400535957290573035651975101657	94908744924191805140028890427294849752798384659407 84501871465439539442324647	76	252.391
28411	20910497 177739217 375536599 145954745454377 73527519400535957290573035651975101657	14978489556623348664825000507994544605575720664053 058445425047068214414649639	77	253.049
28411	20910497 145954745454377 259400137814578063 73527519400535957290573035651975101657	58210682596654230235438631128992478967845543556191 797869437865328343441439279	77	255.008
28411	3409321 20910497 177739217 259400137814578063 73527519400535957290573035651975101657	24167717085996495205619822876229517410634346251120 8677224155911960841679599839	78	257.062
28411	177739217 145954745454377 259400137814578063 73527519400535957290573035651975101657	49479078119304623423271995631758294461551225150779 1787786591318877366290648319	78	258.095
28411	3409321 20910497 375536599 259400137814578063 73527519400535957290573035651975101657	51062801070341804957080878610608658818390703407534 0311778510151890215120810233	78	258.141
28411	375536599 145954745454377 259400137814578063 73527519400535957290573035651975101657	10454195214879884682597258595717436007457759509206 61195359638844893362137784793	79	259.174
28411	3409321 177739217 375536599 259400137814578063 73527519400535957290573035651975101657	43403379078313223905860649653241770923957038533012 05897882210634377456716326313	79	261.228
28411	20910497 177739217 375536599 259400137814578063 73527519400535957290573035651975101657	26620732632888819607887535289055008055272322036365 395345304320661949375120257441	80	263.845
28411	3409321 20910497 177739217 375536599 145954745454377 73527519400535957290573035651975101657	51066478993676671693309835556916468809226021550090 037272214966895651836367721885119	83	274.750
28411	3409321 20910497 145954745454377 259400137814578063 73527519400535957290573035651975101657	19845890260110779688051586931932776738713413640253 9376504029772459093190111204119559	84	276.709
28411	3409321 177739217 145954745454377 259400137814578063 73527519400535957290573035651975101657	16869006009278575803405310341926182023195028448227 96205728369301866301319399417581399	85	279.796
28411	3409321 375536599 145954745454377 259400137814578063 73527519400535957290573035651975101657	35641707284189503325957168272809964646381896107687 79547224719266310682296954588255553	85	280.876
28411	20910497 177739217 145954745454377 259400137814578063 73527519400535957290573035651975101657	10346321145764849701784587948418949210633835088616 925655136154413611211188502802504543	86	282.413
28411	20910497 375536599 145954745454377 259400137814578063 73527519400535957290573035651975101657	21860241767816018401579592807397365848163745784398 633163584141987226114302062500672121	86	283.492
28411	3409321 20910497 177739217 375536599 259400137814578063 73527519400535957290573035651975101657	90758622800693143354382739699216309118009088237343 306024048271823517905534371219007561	86	285.546
28411	177739217 375536599 145954745454377 259400137814578063 73527519400535957290573035651975101657	18581204718578974525351302691493366292131483357406 8749985506241694130634867315222327081	87	286.580
28411	3409321 20910497 177739217 145954745454377 259400137814578063 73527519400535957290573035651975101657	35273929955000163150137933168891640341747357278158 545591494449101567388140397563137591045303	92	304.114
28411	3409321 20910497 375536599 145954745454377 259400137814578063 73527519400535957290573035651975101657	74528581324092275672891738929708794730827469941411 732415903850544031723238422026853976239841	92	305.193
28411	3409321 177739217 375536599 145954745454377 259400137814578063 73527519400535957290573035651975101657	63349291452350388007745228643464855060456000971557 7644769336125438875150196470001099386122001	93	308.281
28411	20910497 177739217 375536599 145954745454377 259400137814578063 73527519400535957290573035651975101657	38854222552423149107543483887656396137151650635060 63874365678310426393558001090354524760269257	94	310.897
28411	3409321 20910497 177739217 375536599 145954745454377 259400137814578063 73527519400535957290573035651975101657	13246651688664984313847925803134859213471000269477 55719421626874298122251155783536857871020594354449 7	101	332.598

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-12-28	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-	skipped known factor: 3409321 skipped known factor: 20910497 skipped known factor: 177739217 skipped known factor: 375536599 skipped known factor: 145954745454377 skipped known factor: 259400137814578063	-	-	0.813	-	-	13.650%
2022-10-12	nordi	sweet16_ccx3	3000000000	3000000000		-	skipped known factor: 3409321 skipped known factor: 20910497 skipped known factor: 177739217 skipped known factor: 375536599 skipped known factor: 145954745454377 skipped known factor: 259400137814578063	-	-	2.396	-	-	11.589%
2023-02-18	nordi	sweet16_30.8b14	3000000000	925584566816910			73527519400535957290573035651975101657	38	125.790	40,280	3.12995e-5	80,560	31.883%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26	ANONYMOUS	Manual testing	?	?	145954745454377	47.053	15	0.000	3.21122e-5	0.001
2008-08-26	ANONYMOUS	Manual testing	?	?	177739217	27.405	9	4.26100e-10	0.000	3.12026e-9
2008-08-26	ANONYMOUS	Manual testing	?	?	20910497	24.318	8	6.26618e-12	0.000	4.58866e-11
2008-08-26	ANONYMOUS	Manual testing	?	?	375536599	28.484	9	5.41888e-10	0.000	3.96811e-9

ECM factoring results:

Total ECM effort:	47.956 GHz-days
Estimated T-Level:	36.477

Digits	B1	Complete	FacMiss
20	11000	323.337	0.000%
25	50000	80.267	0.000%
30	250000	14.904	0.000%
35	1000000	2.298	10.050%
40	3000000	0.295	74.422%
45	11000000	0.033	96.747%
50	44000000	0.003	99.681%

ECM Summary

B1	B2	factor	curves	GHz-days
		259400137814578063	1	0.00000e+0
50000	5000000		162	0.093
250000	25000000		608	1.747
1000000	100000000		11	0.126
3000000	300000000		500	17.24
3000000	339000000		800	28.75

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-04	Matthias Wurtinger	WUR_E6600	50000	5000000						28	0.016
2009-04-04	Matthias Wurtinger	WUR_E6600			259400137814578063	57.848		1		1	-
2009-05-10	Matthias Wurtinger	WUR_E6600	250000	25000000						30	0.086
2010-04-18	James Hintz	10_122109	50000	5000000						3	0.002
2010-04-19	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-20	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-22	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-23	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-24	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-25	James Hintz	14_091909	50000	5000000						32	0.018
2010-04-25	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-26	James Hintz	10_122109	50000	5000000						11	0.006
2011-03-20	James Hintz	17_051310	250000	25000000						11	0.032
2014-11-19	James Hintz	08_04_2014	250000	25000000						567	1.629
2014-11-19	James Hintz	08_04_2014	1000000	100000000						11	0.126
2018-02-18	nordi	nordiputer	3000000	300000000						500	17.24
2021-10-21	nordi	sweet16	3000000	339000000						800	28.75

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 = 3000000000, B2 = 925584566816910 (P-1 stage 2)

B1 = 3000000000 (P-1 stage 1)

B1 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 500000000 (P-1 stage 1)

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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