Factoring humongous Cunningham numbers

[jyb]

I have update the tables and ECMnet server to reflect all factors reported to me through the end of February 22 (GMT). There were 33 new factors found since the last update, of which 25 completed the factorization of their respective numbers. There are now 700 composites remaining in the tables.

The range of SNFS difficulties remains as it was (237 to 310), with the lowest-difficulty numbers being obligatory quartics. However the three lowest-difficulty composites have all been reserved for factoring by NFS@Home, so there will soon be movement on this lower limit. The smallest composite has 168 digits, the result of an ECM factor found anonymously. Speaking of which, since the last update there were 15 factors found, all apparently by ECM, by an anonymous party. Please let me know if this is you, so I can give proper credit.

Here are the factors found since the last update, showing appropriate credit:

3-2	637	C231	11210083662827408571208719884057644815523096005323606042316577378297633080249926066031310669516715008842140187557.	P119	NFS@Home & G Childers	SNFS	2022-01-11
7-4	307	C250	35145131921410732084755973510606824612712017928146249392939.	P192						NFS@Home & S Wellman	SNFS	2022-01-12
5-2	391	C161	18995135190865412375774172273593569036843586208419928212230997445067.	P94					E Hall			GNFS	2022-01-14
3+2	640	C188	4537602344962946986079209567907623164481027954958076568701763841.	P124					S Welman		ECM	2022-01-15
5+2	850L	C196	16147945874995755431375584756413233152575241201218536701.	C141						Yoyo@home		ECM	2022-01-18
5+2	850L	C141	54594778651191687937436560385440359691560304756098829502231973401.	P76					O Kruse			GNFS	2022-01-19
4+3	1293L	C218	9276954705498993089656736518884580920260878572324736587487934383447.	P151					NFS@Home & S Wellman	SNFS	2022-01-20
8+3	326	C193	14376412083313214245755608148968611466088314059645058938641614791489.	P125					NFS@Home & S Wellman	GNFS	2022-01-27
5-4	1055L	C230	134196504733264945875092740372555598608761768772386662711.	P174						Unknown			ECM	2022-01-28
12+5	280	C208	880434094931502894008812802191199980965130318200907814421217921.	P145					NFS@Home & S Wellman	SNFS	2022-01-28
6-5	349	C221	32714025627975316667036818000195577154647830189600201.	C169							Unknown			ECM	2022-01-29
9-5	745M	C277	22639044904258725021315614579088845551882602817294142781791.	C218						Unknown			ECM	2022-01-30
11+9	254	C249	23248037042537083574061799538693333674589317738844242606297.	C191						Unknown			ECM	2022-01-30
4+3	1299M	C242	2045419968486472607168996992084491487610490356833041796491139.	P182						NFS@Home & G Childers	SNFS	2022-01-31
9+8	598L	C210	1977279812773900130020070670167813327157345921778556584853.	P152						Unknown			ECM	2022-02-01
11+6	262	C209	48441488120276911571659444977669503922710170054222650376849.	C151						Unknown			ECM	2022-02-02
3+2	1506L	C203	464492740118873446513380787537268633796370366462789967039515453.	P141					Yoyo@home		ECM	2022-02-02
3+2	548	C257	274022434555434041111465483882171879464922665500507697.	C203							Unknown			ECM	2022-02-04
11+6	262	C151	278046791127374341514296542418834434021190381699649139413927727864817.	P82					T Singer		GNFS	2022-02-08
8+5	335	C189	53389198532979464436956723360541796937483095659223150424971.	P130						NFS@Home & J Becker	SNFS	2022-02-14
10+9	272	C188	539694504945187893368361339439905555431904910939273986516144666700994185881562766421169921.	P99		NFS@Home & G Childers	GNFS	2022-02-15
6-5	349	C189	3117787282893590999572361502471149940428319002796286714196798997173121297064357.	P90			NFS@Home & D Domanov	GNFS	2022-02-17
5-3	373	C225	414909386583412739386811114757555978544647405137565914645983226582546177128195987.	P144			NFS@Home & G Childers	SNFS	2022-02-17
9+5	319	C202	63184752415912095709775607092807641305478411922889721.	P149							Unknown			ECM	2022-02-21
11+9	283	C274	422029286638290277421851951788883505118567678391732620961.	C217						Unknown			ECM	2022-02-21
3+2	577	C203	600389938555109610985606138448814105052336796841292517.	P150							Unknown			ECM	2022-02-21
8+7	332	C243	33363186367696673954651958177865954899749062042905143700217.	P185						Unknown			ECM	2022-02-21
8+7	298	C198	1654174159681075982563878803552635711707202000414432408021637.	P137						Unknown			ECM	2022-02-21
5+4	428	C230	78872452770338686305039010566370206507114666858697870966131361.	C168						Unknown			ECM	2022-02-21
10-3	271	C218	6280009684043146474829217634457037033386666517337628264368561543.	P155					Unknown			ECM	2022-02-22
11-3	251	C236	20147172857070442268241160479148249499984051018320022437.	P181						Unknown			ECM	2022-02-22
9+7	637M	C242	5886180937954016804740429526087580443251414050991362141789675415907153865000631.	P163			NFS@Home & S Wellman	SNFS	2022-02-22
5-4	985M	C192	282320441741448157688234452715934659860545417130430823639119288658533381.	P121				NFS@Home & G Childers	GNFS	2022-02-22

[charybdis]

Have you contacted Ryan Propper? Not sure anyone else here has the interest and firepower to find that many ECM factors in such a short space of time.

Also this should be C169:

Originally Posted by jyb

6-5	349	C189	...	NFS@Home & D Domanov	GNFS	2022-02-17

[ryanp]

Originally Posted by charybdis

Have you contacted Ryan Propper? Not sure anyone else here has the interest and firepower to find that many ECM factors in such a short space of time.

Also this should be C169:

Yeah... most if not all of these were me. I occasionally run ECM on unreserved composites on the list.

I've uploaded the GMP-ECM output here.

[jyb]

Originally Posted by charybdis

Have you contacted Ryan Propper? Not sure anyone else here has the interest and firepower to find that many ECM factors in such a short space of time.

Also this should be C169:

Thanks for the correction! Now fixed on the website.

[jyb]

Originally Posted by ryanp

Yeah... most if not all of these were me. I occasionally run ECM on unreserved composites on the list.

I've uploaded the GMP-ECM output here.

Thanks, Ryan. I assumed it was you, but I hadn't gotten around to reaching out yet. All attributions now fixed on the website.

[jyb]

I have update the tables and ECMnet server to reflect all ECM work and factors reported to me through the end of March 13 (GMT). Thanks to a great deal of ECM work by Ryan Propper, there are a lot of new factors in a fairly short time, a few new small composites suitable for GNFS, and we've hit a major ECM milestone.

There were 43 new factors found since the last update, of which 30 completed the factorization of their respective numbers. There are now 670 composites remaining in the tables.

As of this writing, there are three composites with digit counts in the 170s, the smallest two of which are unreserved. Those are still a reasonably heavy lift for personal work, but certainly within reach for a number of the people on this forum. And if nobody else wants them NFS@Home can make quick work of them, once polynomials are found.

The lower end of the range of SNFS difficulties for both quartics and non-quartics has been slowly but steadily moving up as composites are cracked. The easiest quartics have difficulty 239, with the easiest two already reserved (after which it will be 240). The easiest non-quartics have difficulty 261, a fairly quick job for NFS@Home.

The big ECM news is that all HCN composites have now had at least a t55's worth of work done, with many having received quite a bit more. Ryan has done a good job of clearing out the smaller factors. It's doubtful there are any left with digit counts in the low 50s, and he has managed to find quite a few that are much larger: in the last few days he found a 66-digit prime and two 67-digit primes. All of these are of sufficient size to (currently) make this year's ECM top-10 list. All of which is to say that anybody planning on doing ECM work on these numbers, whether for NFS pre-testing, or just in the hope of finding factors, should target at least the 60-digit level (traditionally a B1 value of 260,000,000).

Here are the factors found since the last update, showing appropriate credit:

3+2	547	C203	1662098259259162316909955020937420876898449550575141427243841252666257729.	P131				NFS@Home & J Becker	SNFS	2022-02-23
8+5	790L	C205	25046922745188590095280159613427823503780674298742359361.	P149						J Becker		ECM	2022-02-23
10+9	670M	C212	416233122567309050480571616077665527640524475572551214301.	P156						R Propper		ECM	2022-02-24
12+7	275	C203	37936595755450417468465357186834290954998004679615912393143761950041726294358911051251.	P118			NFS@Home & G Childers	SNFS	2022-02-24
8-7	289	C231	38879529782623453988291719106936461825611460410751761407.	P175						NFS@Home & G Childers	SNFS	2022-02-27
5-4	995L	C196	36832342625739624260915996697458556925922623588621306541.	C140						R Propper		ECM	2022-02-28
5-4	995L	C140	2535294970259058699423928503374984426126355631280596381929160579831.	P74					R Propper		GNFS	2022-02-28
9+7	313	C232	12773256851773684078933229150974098370229632087985790553.	C176						R Propper		ECM	2022-03-01
7+2	355	C207	345427299310569829939597887915363280696647320341336985378835725552087660145736939962175562561082181.	P109	R Propper		SNFS	2022-03-02
7-3	1239M	C274	510148378557963508667716178505995964095075598855842493373.	P217						J Becker		ECM	2022-03-03
8+3	1014M	C191	2779059060175564193332793046371834401477401401251247144212005604488060320391893717103397.	P104		NFS@Home & G Childers	GNFS	2022-03-03
5+4	428	C168	36423353057163520144029279288369198778201778199941771867099156639061643193.	P95				R Propper		GNFS	2022-03-04
5-2	373	C209	542244277270508418263688291593018882952257717135384183921835568192573358722806534563151911.	P120		NFS@Home & S Wellman	SNFS	2022-03-05
3-2	547	C252	119311408203546960878547419696246898142859958479270486890619848562599184587109.	P175				NFS@Home & G Childers	SNFS	2022-03-05
5-3	425	C193	5545380314234354391960099955343830633252270248263928992325408885074332219104312732536051.	P105		NFS@Home & G Childers	SFNS	2022-03-07
7+2	334	C221	6669467002985742527835023822944174779400432421127338978317667869.	C157					R Propper		ECM	2022-03-08
3+2	548	C203	22920565757039318065355862471201927008431619452353433729.	P148						R Propper		ECM	2022-03-08
10+7	284	C238	251065969755555165239104394191572559611521395360944161.	C185							R Propper		ECM	2022-03-08
11+7	283	C260	1517247848920000782100538582645760028400231187585674016916009.	P200						R Propper		ECM	2022-03-09
10-7	307	C256	94043977777741899197470564156058349774027971706094953899.	P200						R Propper		ECM	2022-03-09
8+7	770M	C208	492281428076152472213044693742790146309973263691875021.	C154							R Propper		ECM	2022-03-09
3+2	1782M	C199	10675961618593591968731109629427541000826457400809226717.	P144						R Propper		ECM	2022-03-10
5+3	1425L	C209	13050936625541149881701476740133992858897724577122390311001.	C150						R Propper		ECM	2022-03-10
5-2	419	C212	1707544125025883963079172713295307931967831778867289839947.	P155						R Propper		ECM	2022-03-10
7+2	334	C157	97025828371271374107803500436849873982936057769180871361913.	P98						R Propper		GNFS	2022-03-10
3+2	1734M	C249	1194942064830734082142474266028110521067260074673718807001.	P192						R Propper		ECM	2022-03-10
8+3	786L	C226	25795021000288471829512722280109368888630885235958163898197774208748622283950178809.	P143			NFS@Home & J Becker	SNFS	2022-03-10
5+3	1425L	C150	649072703119067797125262761477627814121281453855220563016333027104233193201.	P76				R Propper		GNFS	2022-03-10
3+2	584	C275	214667848961962525128477238603743033616551151364287342673.	C219						R Propper		ECM	2022-03-10
5-4	955L	C226	149760408488740394113680189649118204802016915869906128941.	P170						R Propper		ECM	2022-03-11
8+7	770M	C154	14122489438881243993536053566827980838693796952354357543315195004963201.	P84				R Propper		GNFS	2022-03-11
7-5	311	C248	208600915558811280885364342867057319403050609244906742663.	P191						R Propper		ECM	2022-03-11
8+5	298	C264	124546759964666172996971230473949560438283305922114781.	P211							R Propper		ECM	2022-03-11
10+3	1110L	C255	6852307450192640603053480020663072638178711368334044161.	C200						R Propper		ECM	2022-03-12
7+6	353	C232	693840128865908555727847524365571395083304405271873973507.	C175						R Propper		ECM	2022-03-12
11+4	605L	C230	50321945231252245436764106395002517797184367067786766874081.	C171						R Propper		ECM	2022-03-12
11+7	271	C264	61765686971343702074949165535491876261460875836145358949.	P208						R Propper		ECM	2022-03-12
6-5	377	C213	43133122684940862622610953078458929409308024159895500226859.	P155						R Propper		ECM	2022-03-12
6+5	388	C260	2122967513364536861032231406748778237264813525949673409.	C206						R Propper		ECM	2022-03-13
9-2	323	C265	566988876823193134325875141524437774201412303928115105561778328153.	C199					R Propper		ECM	2022-03-13
7+4	847M	C268	1278015782415607237570157407504924953082724220721117520261.	C211						R Propper		ECM	2022-03-13
5-4	397	C239	1025597577713768120437566600643475064496172745752879129428699717961.	P173					R Propper		ECM	2022-03-13
11+5	283	C233	1087385244050074655597234616128393756996508608776071176982863428589.	P167					R Propper		ECM	2022-03-13

[jyb]

The tables and ECMnet server have been updated once again, showing all ECM work and factors reported to me through the end of April 14 (GMT). There were 22 new factors found since the last update, of which 20 completed the factorization of their respective numbers. There are now 650 composites remaining in the tables.

There is a 181-digit composite, currently reserved by NFS@Home. Other than that, all composites are now at least 190 digits in size. SNFS difficulties start at 242 for quartics and 261 for non-quartics. None of these make for easy NFS jobs, so collective efforts are probably the best bet for finding new factors, other than ECM, of course.

Speaking of which, Ryan has continued to run a lot of ECM on these numbers, pushing up curve counts and finding a number of factors along the way, detailed below. As mentioned with the last update, ECM work needs to be done at fairly high B1 (at least 260M) to have any reasonable hope of finding a factor.

Here are the factors found since the last update, showing appropriate credit:

8-5	289	C236	14671349769058184512947349587565899843280167256636598637366856189409866951307.	C160				NFS@Home & J Becker	SNFS	2022-03-15
8-5	289	C160	42478531839212333780160951486896404364576351716782115494742107305937139284152147.	P80			NFS@Home & J Becker	SNFS	2022-03-15
11+9	251	C220	12509539700751732567799212224203534942256862923559959185879457830872563.	P150				NFS@Home & G Childers	SNFS	2022-03-21
9+7	313	C176	478529773719783498777323282692856926137420897926609156792413897231.	P111					NFS@Home & G Childers	GNFS	2022-03-22
9-5	625M	C239	6372547713579263195051996798667741960130358491868297870416155918642597151417501.	P160			NFS@Home & G Childers	SNFS	2022-03-22
3+2	625	C214	1450181952204171571735738386675395214517112248112291804812090253101150299563246963961848462666987501.	P114	NFS@Home & J Becker	SNFS	2022-03-23
12+7	277	C233	894232871762840509826816108759516121944419931808976721.	P179							R Propper		ECM	2022-03-23
11-9	251	C242	37487915558202647106146410545259384810678362470155118104937157398846663837748156791277652962946657.	P144	NFS@Home & G Childers	SNFS	2022-03-27
11+8	251	C245	2123732063576502378231401288360828302458894275070876225726909121410282073243082773429.	P161			NFS@Home & G Childers	SNFS	2022-03-30
11-3	759M	C191	467283369823474221379480607727590712546991895138390123444102114104508423391946480242612061.	P102		NFS@Home & G Childers	GNFS	2022-03-31
11+4	605L	C171	6119581385551216735796820050477663665570702236812349830342555435567449951.	P98				NFS@Home & J Becker	GNFS	2022-03-31
7-4	355	C237	82435894365954059743874507746877626872562178066695111871125620225193533666831195194687427382900832038701641.	P130	NFS@Home & J Becker	SNFS	2022-04-01
7+6	353	C175	166637691772532139931768612667142592490497378108602624662098639.	P113					NFS@Home & S Wellman	GNFS	2022-04-01
8+3	978M	C231	1216926574302980876045729245609387776602122073166351105656075197.	P168					R Propper		ECM	2022-04-03
10+7	284	C185	188194761556146005743278446158882956037161175329692796065615273770177.	P117					NFS@Home & W Wellman	GNFS	2022-04-05
7+4	313	C207	265457763615950619142923586721615527694918178664243701825097.	P148						R Propper		ECM	2022-04-05
3+2	592	C246	71746140023303170317464975438623886902075928866445447617.	P191						R Propper		ECM	2022-04-06
9+7	304	C233	32827182188865081271094047334474157859406328696210593.	C181							R Propper		ECM	2022-04-06
4+3	496	C289	6311536068026748744332614217223703561529324854669427215684001.	P229						R Propper		ECM	2022-04-07
10+9	283	C194	1169181054943523682289460045653272322899612138896405298760459367479651294391073821537237978801.	P101		NFS@Home & G Childers	GNFS	2022-04-08
11+8	295	C198	13697052410634044421040590874088927755882762978681003373035861.	P136						R Propper		ECM	2022-04-13
5+3	436	C280	4287425480932559686655288228228995450869963232958709766121.	P223						R Propper		ECM	2022-04-14

[BudgieJane]

Originally Posted by jyb

Here are the factors found since the last update, showing appropriate credit:

10+9	293	C194	1169181054943523682289460045653272322899612138896405298760459367479651294391073821537237978801.	P101		NFS@Home & G Childers	GNFS	2022-04-08

This one is third from bottom in the list. It should say

10+9	283	C194	1169181054943523682289460045653272322899612138896405298760459367479651294391073821537237978801.	P101		NFS@Home & G Childers	GNFS	2022-04-08

[jyb]

Originally Posted by BudgieJane

This one is third from bottom in the list. It should say

10+9	283	C194	1169181054943523682289460045653272322899612138896405298760459367479651294391073821537237978801.	P101		NFS@Home & G Childers	GNFS	2022-04-08

You're absolutely correct. This was wrong in the report and in the UPDATE file, but it was correct in the actual 10+9 table. I've corrected the UPDATE file (and the report, above); the change will appear in the next update.

Thank you! It's good to know there are still eyes on these reports. This is actually good timing, because I've actually found a whole bunch of other mistakes while I've been preparing for an overhaul in the table format. More on that soon.

[jyb]

I've updated the tables and ECMnet server to show all ECM work and all factors reported to me through the end of May 8 (GMT). There were 34 new factors found since the last update, of which 25 completed the factorization of their respective numbers. There are now 625 composites remaining in the tables. Digit counts and SNFS difficulties have much the same range as before, with a couple of smaller composites (left by ECM hits) already reserved for GNFS.

Ryan Propper has once again found the bulk of the factors in this update, both through ECM and NFS. He currently has 5 more composites reserved for NFS, and is continuing to throw his considerable resources at ECM (two more factors were found by ECM today). NFS@Home has another 6 composites reserved for NFS.

A few factors with digit counts in the 50's have been found, the smallest being a 54-digit factor of 7+2,359. But there probably aren't many more of those around. Anybody running ECM on these numbers is advised to use high B1 values (260M or greater).

Here are the factors found since the last update, showing appropriate credit:

3+2	1674L	C192	314534146901137451329638216473219906426945703166112022113211793124315149.	P120				NFS@Home & J Becker	GNFS	2022-04-15
11-7	251	C247	362385828049049380503972660031359669047821607528244015962886052631803085931248597950175027713899698712337.	P142	NFS@Home & S Wellman	SNFS	2022-04-17
11+9	257	C264	10031515388934411933937954911372014809222358568678460699817.	C206						R Propper		ECM	2022-04-18
3+2	589	C231	71603719042454947729203407508429813400123153761614653757.	C175						R Propper		ECM	2022-04-18
5+2	1090M	C194	3100622699854972303590957488160026679182779473653469683892664607901520221425321899141.	P109			NFS@Home & G Childers	GNFS	2022-04-20
9-2	311	C221	1053901648185913873788527948016549473287423178271200319988927223.	C158					R Propper		ECM	2022-04-20
8-7	319	C205	91230119418088085881016669773354395927476321787305273345377172905946089536183115548810399928173317027.	P104	NFS@Home & G Childers	SNFS	2022-04-21
11-6	251	C248	5681800633059770170579322866990000664123436303476040743240250781305250087847131609203962422950191915432338514230351187.	P130	NFS@Home & J Becker	SNFS	2022-04-22
7+6	364	C203	125287984058712598386997626539607435582015874208413505609.	P147						R Propper		ECM	2022-04-24
9-2	311	C158	3743585832610109049090738151474192520288721953953700009756565462925489543.	P86				R Propper		GNFS	2022-04-23
9+7	304	C181	12511587720257212449876982118787904710846786110270778816257323828438549791017116422978602658049.	P95	NFS@Home & G Childers	GNFS	2022-04-27
4-3	487	C225	108753968071631988400408845938746878085413457066196766049.	C169						R Propper		ECM	2022-04-30
10-7	293	C279	469571117118764764647982066952046533759010443871280324501.	C223						R Propper		ECM	2022-04-30
11+9	290	C213	34616130269409724747538795191277042546112009607611597966771684307183298857158051661.	P130			R Propper		SNFS	2022-05-01
9+8	323	C271	52462254442786725150586223873354651822675754909627435521.	C215						R Propper		ECM	2022-05-01
7+3	311	C256	2446480523912620817130037639110977931015515326424225228614789.	P196						R Propper		ECM	2022-05-02
7+5	311	C199	108574711032875785326845938394230548120252051659871598931621224041798295523.	P125				R Propper		SNFS	2022-05-02
11+2	290	C215	50267237410312261961211546530594779245247625536499864923121.	P156						R Propper		ECM	2022-05-03
11-10	271	C217	4423750505980632306404460873903829595846518865124085903.	P162						R Propper		ECM	2022-05-03
7+6	311	C242	37603778808819717180594018282987258833629266710554534040057819009425226767523090867147849.	P153		R Propper		SNFS	2022-05-03
7+2	359	C288	321419477257335721086135658781773770585741527013382709.	C235							R Propper		ECM	2022-05-03
7-4	311	C263	3240420504787025091754186046574246126563941642760475204089776445715840109.	P190				R Propper		SNFS	2022-05-03
7+6	313	C218	1438525602714988123151480637844172632828787396170106832311.	P161						R Propper		ECM	2022-05-04
4+3	1419L	C218	11995895159268474048186109429306443254181202002879195788257.	P160						R Propper		ECM	2022-05-05
7+4	311	C238	263757164984434144042413391759675064501502956564130400953077.	C179						R Propper		SNFS	2022-05-05
7+4	311	C238	36554699708003070672593819159128005287740813409456588629339044178157.	P111					R Propper		SNFS	2022-05-05
9+2	634M	C281	1029712148136867102430824433026177951086641720191430873461833.	P221						R Propper		ECM	2022-05-05
7+3	341	C201	91605519755084956973312868491458346296185026127074218445285709621332549439717615228313.	P115			R Propper		SNFS	2022-05-06
7-2	341	C214	170106575048192195859616302720987899424902000504319611970376820912354276579.	P139				R Propper		SNFS	2022-05-06
9+2	299	C253	457594012406457074400675952548903974817273913272588047455913448568441458270515911624002956530821661276767636631843.	P139	R Propper	SNFS	2022-05-07
9-5	299	C207	14082544310027170269299604884495176557697181551305869826422385893559690697843702619695969847478415317329.	P104	R Propper	SNFS	2022-05-08
11+4	292	C257	62222190167684771299609438077087859849378780796931113986441.	C198						R Propper		ECM	2022-05-08
9+7	299	C242	7389323357141081358458872103921949720066158232667072227870494842897.	P175					R Propper		SNFS	2022-05-08
9+5	304	C227	4859992023024065746596378488711517209622519353338566594983419937.	P163					R Propper		ECM	2022-05-08

[jyb]

I have been considering making some changes to the format of the tables as they are shown on the website. The changes largely fall into the following categories:

• Show which algebraic factors contribute to each number, by displaying the appropriate exponents in parentheses, as is done in the Cunningham tables.
• Show intrinsic factors, which are currently omitted from the non-Aurifeuillian entries (I'm not really sure why).
• Include a link to the full expansion of ultimate primes and composites which aren't explicitly shown in the tables (because they appear as e.g. P137).

The reason I wish to make this change is that I want to make the tables more understandable for those are not already well versed in how they work. The first of the above changes is therefore the most important: it was by studying the algebraic components of the numbers in the Cunningham tables that I really came to understand how algebraic factors work in cyclotomic forms, especially for Aurifeuillian factorizations. I want others to have an easier time figuring that out for the HCN's than I did when I first started looking at them. The other changes are more minor, and are mostly aimed at ensuring that it is possible to discover all of the factors of a given HCN just by looking at the tables and primes/composites tables, without having to do any calculations.

To be concrete and see what this might look like, you can see the current implementation here. Note the link on the main page to a new page that describes the format, as well as links to the primes/composites tables. And of course each of the individual tables has been updated to show the algebraic components of each entry.

So here are some questions for the forum:

1. Does anybody care about this?
2. Are there any objections to making changes of this nature? If so, what is the specific complaint?
3. I've never really understood why intrinsic factors are marked as they are in the Cunningham tables, but I'm doing it the same way just because it's done there. Are there opinions about that?
4. Are there any suggestions for further changes that people would like to see?

Thanks for any comments, suggestions, critiques, etc.