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OEIS sequences needing factors
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Please check with corresponding OEIS entry and with factordb.com to make sure number still needed before embarking on a significant effort.
Contents
Mersenne Forum
Many of the listed sequences were subject to factoring efforts at Mersenneforum.org, a discussion board for those interested in factorization and primality searches. In particular, there is a thread about sequences that require some factorization in order to be extended, which comes with the comment:
- The following table lists some OEIS entries for which computing further terms is blocked by finding at least one factor of an integer. In some, cases a complete factorization is required, in others only the smallest factor, or any factor.
- The list is unlikely to be exhaustive nor does inclusion or exclusion from the list indicate any kind or importance or mathematical utility. As near as I can tell many of these sequences have no utility beyond their OEIS entry.
- Rows marked with "*" indicate more terms are needed for the initial sequence lines in the corresponding OEIS entry. That is, the OEIS entry has (or should have) the "more" keyword. As above, it is not an indication of the importance of the sequence.
- In some cases it is possible or likely that considerably more ECM effort has been expended than is indicated below.
ECM efforts
Sources
The following list contains some websites that track ECM or other factoring effort, which may not always be reflected on this page, but often are the sources of the ECM effort listed here:
- yoyo@home performs ECM on a wide range of cofactors.
- The most wanted Cunningham numbers can generally be assumed to have t70 ECM performed on them, as well as most base 2 Cunningham cofactors.
- mersennus.net tracks ECM efforts on Fibonacci and Lucas numbers.
- Studio Kamada tracks ECM efforts for near-repdigit-related numbers.
- factordb does not track unsuccessful ECM efforts, but t-level of approximately the size of the largest known prime factor can be assumed at the least, barring their existence being known solely due to other methods (such as algebraic factorization, which may or may not be reflected accurately on factordb's "more information" subtab).
- Some forms with known algebraic factorizations for a subset of their numbers:
- Cunningham and Homogeneous Cunningham numbers (algebraic and Aurifeuillean)
- Fibonacci and Lucas numbers (Aurifeuillean and via other identities)
- Some forms with formulae for their divisors:
- Fermat numbers (Fermat divisors)
- It can be assumed a large amount of ECM has been run on all Fermat cofactors
- Fermat divisors are primarily found through Proth Prime searches
- Fermat numbers (Fermat divisors)
- Some forms with known algebraic factorizations for a subset of their numbers:
The ECM efforts on this wiki page likely include efforts from the above links, and as such should not be backpropagated to those sources as if they had occurred twice. To be on the safe side, the total effort for a given composite number should be estimated as `max(other source, this page)`, unless a high degree of provenance can be established.
T-levels
To simplify communication of ECM progress, many use the "t-level" metric to condense the [<curves>@<B1>, ...] format down to a single number. For instance, the factoring program yafu can be used with the command line arguments -work <t1> and -pretest <t2> to run an optimal number and size of ECM curves on a composite with existing ECM t1 and desired finishing ECM t2.
Here's yafu's explanation of t-levels:
- A note on the “t-level” terminology used in factor(). Something that has received, say, "t30", has had enough ecm curves run on it so that the probability that a factor of size 30 has been missed is exp(-1) (about 37%). Likewise, t35 indicates that factors of size 35 are expected to be missed about 37% of the time (at which point a 30 digit factor would only be expected to be missed ~5% of the time). t-levels are calculated from tabulated data extracted by A. Schindel from GMP-ECM in verbose mode. See also the GMP-ECM README file. I am unaware if t-level is universally accepted terminology or not, but others frequently use it (mersenneforum.org), and it is a handy way to talk about how much a particular number has been tested with ecm.
Conversion of ECM effort from <curves>@<B1> form to t-level form can be performed easily on Mersenneforum.org user WraithX's web page: ecmprobs.html.
Sequences in the OEIS
Cunningham numbers
Cunningham numbers are of the form , which have particular importance in number theory. More generally, b here may be fractional, giving rise to numbers of the form . Further extending this to quadratic irrational b leads to values of Lucas sequences (including Fibonacci, Lucas, and Pell numbers).
Cunningham numbers admit factorization via cyclotomic polynomials , and thus factorization of Cunningham numbers reduces to that of values of the corresponding cyclotomic polynomials.
id size description known ecm effort -------------------------------------------------------------------------------- b = 2 A002185 C338 2^1123+1 or Phi_{2246}(2) t65 [likely more], also needed by A002587, A002589, A046798, A046799, A053285, A054992, A057957, A059886, A069061, A085029, A086257, A112092, A250291, A274906, A295501, A366602, A366603, A366604 A002590 C311 2^1124+1 or Phi_{2248}(2) t65 [likely more], also needed by A057940, A274903, A366605, A366606, A366607, A366608 A283931 C236 * 2^1151+1 or Phi_{2302}(2) t65 [likely more], A002184 C337 2^1207-1 or Phi_{1207}(2) t65 [likely more], also needed by A002588, A005420, A046051, A046800, A046801, A049093, A049094, A053287, A059499, A075708, A085021, A086251, A097406, A112927, A237043 A003260 C297 2^1213-1 or Phi_{1213}(2) t65 [likely more], also needed by A046932, A055061, A088863, A100730, A181046 A038553 C284 2^1229-1 or Phi_(1229)(2) t65 [likely more] A016047 C303 2^1237-1 or Phi_(1237)(2) t65, also needed by A049479, A136030, A186283, A186522, A212953 A006514 C385 2^1277-1 or Phi_{1277}(2) 112000@26e7 [likely more], also needed by A085724 A057953 C212 2^1503-1 or Phi_{1503}(2) t60 [likely more], also needed by A059890, A085033, A274908, A366651, A366652, A366653, A366654 A057936 C248 2^1509+1 t60 [likely more], also needed by A274905, A366655, A366656, A366657, A366658 A345460 C429 * 2^1559+1 A002586 C1156 2^3968+1 t30 [likely more], also needed by A366609 A073639 C984 * 2^4495-1 or Phi_{4495}(2) t65 [likely more] A096393 C1201 * 2^4844+1 or Phi_{9688}(2) t15 A133485 C1510 2^5099-1 or Phi_{5099}(2) t30 [likely more] A133485 C1527 2^5099+1 or Phi_{10198}(2) t30 [likely more] A161508 C2941 2^9983-1 or Phi_{9983}(2) A219461 Cmany * 2^21700-1 or Phi_{21700}(2) A046052 C1133 2^(2^12)+1 or or Phi_{8192}(2) t55, also needed by A050922, A023394, A070592, A321213 A255770 C1221 * 2^(3*2^11)+1 or Phi_{3*2^12}(2) also needed by A255771 A366671 C4880,C9844 2^(3*2^14)+1 or Phi_{3*2^15}(2) A093179 C315653 * 2^(2^20)+1 or Phi_{2097152}(2) A199295 C5050446,C10100891 * 8^(8^8)+1 or 2^50331648+1 or Phi_{100663296}(2) -------------------------------------------------------------------------------- b = 3 A002591 C265 3^691-1 or Phi_{691}(3) t60 [likely more], also needed by A057952, A057958, A059885, A059891, A074477, A085028, A085034, A133801, A295500, A366575, A366576, A366660, A366661, A366662, A366663 A002592 C277 3^692+1 or Phi_{1384}(3) t60 [likely more], also needed by A057935, A057941, A074476, A274909, A366577, A366578, A366579, A366580, A366664, A366665, A366666, A366667 A143663 C265 3^731-1 or Phi_{731}(3) t45 A235365 C321 3^769+1 or Phi_{1538}(3) t60 [likely more], also needed by A272069 A235366 C300 3^797-1 or Phi_{797}(3) t60, also needed by A218356 A275377 C466 3^(2^10)+1 or Phi_{2048}(3) t35 A113913 C317 * 3^2187+1 or Phi_{4374}(3) t60 A200918 C479894 * (3^1006002-1)/1006003^2 or Phi_{1006002}(3) 2@1000,1@2000,1@5000,1@10000 -------------------------------------------------------------------------------- b = 10 A003021 C295 10^332+1 or Phi_{664}(10) t60, also needed by A057934, A119704, A344897, A366668, A366669 A269503 C300 10^346+1 or Phi_{692}(10) t40 A001270 C328 10^353-1 or Phi_{353}(10) t60, also needed by A003020, A005422, A046053, A046107, A046412, A046415, A046416, A046417, A046418, A046419, A046420, A057951, A059892, A061075, A070528, A070529, A081317, A081318, A085035, A095370, A095413, A095414, A095417, A095418, A102146, A102347, A102380, A112505, A147556, A295503 A176973 C230 10^383-1 or Phi_{383}(10) t60 A087020 C350 10^428+1 or Phi_{856}(10) t60, also needed by A087021, A087022, A087023, A087024, A087025, A087026. A003060 C336 10^439-1 or Phi_{439}(10) t60, also needed by A007138 A046414 C449 10^467-1 or Phi_{467}(10) t40, also needed by A046430, A095415, A268582 A147554 C252 * (10^477-1)/(10^159-1) or Phi_{477}(10) t55, also needed by A110758 A046413 C509 10^509-1 or Phi_{509}(10) t40, also needed by A196104 A072848 C315 10^528+1 or Phi_{1056}(10) t45 A275381 C473 10^(2^9)+1 or Phi_{1024}(10) t35 A038371 C950 10^(2^10)+1 or Phi_{2048}(10) t35 A102050 C16385 * 10^(2^14)+1 or Phi_{32768}(10) 200@1e6, also needed by A185121 A122787 C354295 Phi_{3^12}(10) or Phi_{531441}(10) A076670 Cbig (10^9)^(10^9)+1 or Phi_{18000000000}(10) -------------------------------------------------------------------------------- other integer b A057939 C317 5^472+1 or Phi_{944}(5) t45, also needed by A074478, A366615, A366616, A366617, A366618 A057956 C260 5^503-1 or Phi_{503}(5) t60, also needed by A059887, A074479, A085030, A295502, A366611, A366612, A366613 A275378 C329 5^512+1 or Phi_{1024}(5) t40 A250291 C364 5^521-1 or Phi_{521}(5) t60, also needed by A218357 A057955 C281 6^421-1 or Phi_{421}(6) t60, also needed by A059888, A085031, A274907, A366620, A366621, A366622, A366623 A057938 C246 6^421+1 or Phi_{842}(6) t60, also needed by A274904, A366627, A366628, A366629, A366630 A275379 C777 6^1024+1 or Phi_{2048}(6) t25 A366670 C3126 6^4096+1 or Phi_{8192}(6) A057937 C314 7^388+1 or Phi_{776}(7) t45, also needed by A227575, A366636, A366637, A366638, A366639 A057954 C299 7^389-1 or Phi_{389}(7) t60, also needed by A059889, A074249, A085032, A366632, A366633, A366634, A366635 A218358 C315 7^431-1 or Phi_{431}(7) t40 A275380 C861 7^1024+1 or Phi_{2048}(7) t20 A274910 C319 11^317-1 or Phi_{317}(11) t40, also needed by A366681, A366682, A366683, A366684, A366685 A062308 C334 11^326+1 or Phi_{652}(11) t40, also needed by A366686, A366687, A366688, A366689, A366690 A218359 C344 11^331-1 or Phi_{331}(11) t40 A275382 C482 11^512+1 or Phi_{1024}(11) t35 A366712 C304 12^307+1 or Phi_{614}(12) t40, also needed by A366713, A366714, A366715, A366716, A366720 A250288 C335 * 12^311-1 or Phi_{311}(12) t60, also needed by A252170, A366707, A366708, A366709, A366710, A366711, A366718 A275383 C553 12^512+1 or Phi_{1024}(12) t30,4600@11e6,1000@11e7 also needed by A366719 A302097 C184 13^256+1 or Phi_{512}(13) t57 A218360 C308 13^417-1 or Phi_{417}(13) t45 A302098 C265 14^256+1 or Phi_{512}(14) t45 A324941 C239 17^212+1 or Phi_{424}(17) t45 A218361 C200 17^243-1 or Phi_{243}(17) t45 A218362 C254 19^239-1 or Phi_{239)(19) t45 A218363 C381 23^307-1 or Phi_{307)(23) t35 A218364 C262 29^223-1 or Phi_{223)(29) t45 A128677 C21101 (102^(103^2)+1)/(102^103+1) or Phi_{21218}(102) A006486 C282 139^139-1 t45, also needed by A334167, A354226 A007571 C242 149^149+1 or Phi_{298}(149) t45, also needed by A344859, A115973 A177996 C408 192^193+1 or Phi_{386}(192) t40 A298310 C322 * 656811^99+1 or Phi_{198}(656811) t45 A298398 C276 * 2746511^90+1 or Phi_{180}(2746511) t45 -------------------------------------------------------------------------------- fractional b A082869 C312 * 3^653-2^653 or Phi_{653}(3, 2) t46 A122119 C680 * 2^1024+5^1024 or Phi_{2048}(2, 5) 100@10000,440@1e6 [1 factor is known, swellman] -------------------------------------------------------------------------------- irrational b A060385 C276 Fibonacci(1423) 20158@11e7, 2000@26e7 A072381 C323 Fibonacci(1543) 20158@11e7, 2000@26e7 (also needed by A278637) A001578 C258 Fibonacci(1453) 20158@11e7, 1000@26e7 (also needed by A060383, A139044) A099954 C377 * F(1801) [F^R(1801) is semiprime] 20158@11e7, 6500@26e7, 650@85e7 (also needed by A072381) A152012 C10449 F(49999) A085726 C383 Lucas(1831) 20158@11e7, 1000@26e7 A115101 C387 * Lucas(2602) 7771@43e6 A246556 C228 Pell(631) 7550@43e6 A250292 C271 * Pell(709) 17768@11e7
Near powers, factorials, and primorials
id size description known ecm effort -------------------------------------------------------------------------------- near-powers with b = 2 A099441 C191 * 2^634-635 t45 A114970 C181 * 2^741+741^2 t45 A099481 C249 * 2^827-827^2 t45 A242273 C350 * 2^1152*1152-1 t40 A242175 C425 * 2^1528*1528+1 t40 A252657 C260 * 4^483-483 t45 A242335 C266 * 4^437*437-1 t45 A242204 C333 * 4^547*547+1 t40 A252789 C461 * 4^765+765 t40 A252661 C334 * 8^369-369 t40 A242271 C439 * 8^483*483+1 t40 A242339 C526 * 8^579*579-1 t40 A085745 C373 * 2^1239+1239 7771@43e6 A165767 C449 * 2^1489-1489 4590@11e6 also needed by A165768, A165769 A289117 C249 * 2^817*155+1 t45 A100497 C436 * (2^361+1)^4-2 t40 A268574 C258 * (2^428+1)^2-2 t45 A269264 C232 * (2^385-1)^2-2 t45 A360993 C367 * (2^406-1)^3+2 t40 A360994 C321 * (2^355+1)^3-2 t40 A268110 C327 * (2^543-542)*2^543+1 t41 -------------------------------------------------------------------------------- near-powers with b = 3 A252788 C669 * 3^1402+1402 904@1e6,450@3e6 A114971 C205 * 3^428+428^3 t45 A081715 C246 * 3^514+2 4590@11e6,1000@11e7 A252656 C299 * 3^626-626 t45 A080892 C314 * 3^658-2 t45 A242274 C417 * 3^866*866-1 t35 A242203 C430 * 3^894*894+1 2350@3e6,1164@11e6 A242340 C492 * 9^512*512-1 t40 A242272 C492 * 9^512*512+1 t40 A252662 C239 * 9^250-250 t45 A252794 C342 * 9^436+436 t43 -------------------------------------------------------------------------------- near-powers with b = 5 A242336 C376 * 5^534*534-1 t40 A252790 C536 * 5^766+766 t40 A252658 C568 * 5^812-812 t35 A114973 C607 * 5^868+868^5 t35 A242205 C707 * 5^1006*1006+1 t35 -------------------------------------------------------------------------------- near-powers with b = 6 A252791 C261 * 6^335+335 t45 A242269 C342 * 6^436*436+1 t40 A242337 C332 * 6^423*423-1 t40 A252659 C481 * 6^617-617 t40 -------------------------------------------------------------------------------- near-powers with b = 7 A252660 C325 * 7^384-384 t40 A114974 C432 * 7^510+510^7 t40 A242270 C612 * 7^720*720+1 t35 A242338 C431 * 7^506*506-1 t40 -------------------------------------------------------------------------------- near-powers with b = 10 A252795 C218 * 10^217+217 t45 A252663 C269 * 10^269-269 t45 A216378 C417 * 10^414*414+1 t40 A242341 C599 * 10^596*596-1 t35 A072288 Cbig * 10^(10^100)+2, need factor > 16 A078814 Cbig * 10^(10^100)-7, need factor > 16 -------------------------------------------------------------------------------- near-powers with b > 10 A099497 C414 * 182^183-183^182 t40 A309747 C561 * 236^236+235^235 t35 A219978 C237 * 115^115-114^114 t45 A259026 C398 * 290*23^290-1 t40 -------------------------------------------------------------------------------- near-factorials A181186 C187 (2^104-1)*104!+1 t45 A095194 C190 1000*114!+157 t45 A095194 C189 1000*115!+167 4480@11e6,1200@43e6 A085747 C171 106!+139 t53 A152089 C174 4*109!+1 t54 also needed by A180590 A100013 C178 110!+7 t55 A063684 C182 * 118!+2 17900@11e7,2000@26e7 A002582 C214 136!-1 17900@11e7 also needed by A054991, A064145, A093082 A083340 C219 75!^2+1 10908@2e8 also needed by A083341 A286181 C222 * 139!-1 4480@11e6,3300@43e6 also needed by A286208 A002583 C242 140!+1 17900@11e7,33500@85e7,1050@3e9 also needed by A054990, A064144, A064295, A078778, A181764 A078781 C272 * 154!-1 t45 also needed by A080802 A098594 C2356 * 929!+1 4590@11e6 A096225 C106520655 * 15750503!+1 -------------------------------------------------------------------------------- near-primorials A002585 C196 523#+1 2350@3e6,262@11e6,17900@11e7 also needed by A054988 A002584 C213 541#-1 t54 also needed by A054989 A065314 C177 438#-439 [factored] also needed by A065316 A065315 C180 442#+443 t54 also needed by A065317 A250293 C359 * 859#+1 t40 also needed by A085725 A250294 C458 * 1091#-1 4480@11e6 -------------------------------------------------------------------------------- other near-products of primes A104358 C190 A104357(182) t45 A104359 C184 A104357(162) t57 also needed by A104360, A104361, A104362, A104363 A104366 C203 A104365(171) t45 A104367 C174 A104365(159) t54 also needed by A104368, A104369, A104370, A104371
Recurrence sequences involving factorization
id size description known ecm effort -------------------------------------------------------------------------------- Euclid-Mullin sequences A000945 C335 EuclidMullin52 t58 also needed by A056756, A051318 A051308 C347 EuclidMullin[5]58 7771@43e6 A051309 C313 EuclidMullin[11]56 7771@43e6 A051310 C204 EuclidMullin[13]37 t45 A051311 C232 EuclidMullin[17]31 t45 A051312 C284 EuclidMullin[19]51 t45 A051313 C355 EuclidMullin[23]38 t40 A051314 C390 EuclidMullin[29]57 t40 A051315 C240 EuclidMullin[31]38 t45 A051316 C247 EuclidMullin[37]43 t45 A051317 C362 EuclidMullin[41]38 t40 A051319 C194 EuclidMullin[47]36 t45 A051320 C283 EuclidMullin[53]49 t45 A051321 C258 EuclidMullin[59]49 t45 A051322 C416 EuclidMullin[61]43 t35 A051323 C200 EuclidMullin[67]43 t45 A051324 C287 EuclidMullin[71]45 t45 A051325 C439 EuclidMullin[73]45 t35 A051326 C292 EuclidMullin[79]32 t45 A051327 C296 EuclidMullin[83]65 t45 A051328 C743 EuclidMullin[89]79 4590@11e6 A051330 C261 EuclidMullin[97]52 t45 A051331 C334 EuclidMullin[131071]37 t40 A051332 C285 EuclidMullin[65537]71 t48 A051333 C168 EuclidMullin[257]45 t52 A051334 C328 EuclidMullin[8191]60 4590@11e6 A051335 C564 EuclidMullin[127]66 4590@11e6 A093782 C429 * EuclidMullin[8581]31 4590@11e6 A094152 C362 EuclidMullin[32687]51 t40 A261703 C183 EuclidMullin[139]35 t45 -------------------------------------------------------------------------------- aliquot sequences A008892 C209 A008892(2146) t45 A014360 C185 A014360(1142) [factored] A014361 C197 A014361(3486) t60 A014362 C182 A014362(1008) [factored] A014363 C192 A014363(1035) [factored] A014364 C181 A014364(2194) t55 A014365 C176 A014365(3839) t55 A152466 C1022 A152466(113)+1 t20 -------------------------------------------------------------------------------- A000946 C332 prod(A000946(k),k=1..14)+1 1000@85e7 A005265 C367 prod(A005265(k),k=1..68)-1 4590@11e6 A005266 C211 prod(A005266(k),k=1..14)-1 17900@11e7 A057204 C1314 4*prod(A057204(k),k=1..47)^2+3 1000@1e6 A057205 C345 4*prod(A057205(k),k=1..24)-1 4590@11e6 A057206 C259 6*prod(A057206(k),k=1..17)-1 17900@11e7 A057207 C572 4*prod(A057207(k),k=1..41)^2+1 7600@43e6 cf. http://mersenneforum.org/showpost.php?p=334311&postcount=60 A057208 C414 prod(A057208(k),k=1..18)^2+4 1800@11e6 A084599 C211 prod(A084599(n),n=1..14)-1 t55 A102926 C472 prod(A102926(k),k=1..111)-1 2300@11e7 A102926 C432 prod(A102926(k),k=1..111)+1 2060@11e7 A124984 C923 prod(A124984(n),n=1..15)^2+2 t20 A124985 C257 8*prod(A124985(n),n=1..12)^2-1 t45 A124986 C554 * 4*prod(A124986(n),n=1..14)^2+1 t35 A124987 C366 * prod(A124987(n),n=1..15)^2+4 t40 A124988 C1197 * 4*prod(A124988(n),n=1..21)^2+3 t15 A124989 C853 100*prod(A124989(n),n=1..14)^2-5 t20 A124990 C224 * Phi_{12}(prod(A124990(n),n=1..8)) t45 A124991 C928 Phi_{5}(5*prod(A124991(n),n=1..34)) t20 A124992 C561 Phi_{7}(7*prod(A124992(n),n=1..21)) t35 A124993 C971 Phi_{11}(11*prod(A124993(n),n=1..14)) t20 A125037 C2117 Phi_{13}(13*prod(A125037(n),n=1..25)) 1000@1e6 A125038 C1164 * Phi_{17}(17*prod(A125038(n),n=1..14)) 1000@1e6 A125039 C745 (2*prod(A125039(n),n=1..29))^4+1 4590@11e6 A125040 C593 * (2*prod(A125040(n),n=1..10))^8+1 4590@11e6 A125041 C1056 (2*prod(A125041(n),n=1..20))^4+1 1000@1e6 A125042 C193 * (2*prod(A125042(n),n=1..4))^8+1 17900@11e7 A125043 C1057 * Phi_{9}(3*prod(A125043(n),n=1..21)) 1000@1e6 A125044 C2958 Phi_{27}(3*prod(A125044(n),n=1..23)) 1000@1e6,4590@11e6[need to confirm smallest before moving on] A125045 C347 * prod(A125045(n),n=1..64)+2 4590@11e6 A217759 C561 4*prod(A217759(n),n=1..51)^2-1 890@43e6 A218467 C276 prod(A218467(n),n=1..19)+1 t45 -------------------------------------------------------------------------------- A031439 C341 A031439(24)^2+1 17900@11e7 A031440 C199 A031440(23)^2-2 17900@11e7 A031442 C187 A151799(A031442(21))*A031442(21)-1 17900@11e7 A034970 C522 A034970(34)*A034970(35)-1 t30 A037274 C251 A037276^{118}(49) t61 A048986 C189 A048985^{281}(2295) t45 A062962 C228 * A001697(13) t51 A082021 C194 A151799^{2}(A082021(22))*A082021(22)+2 t45 A082132 C356 A151799(A082132(22))*A082132(22)-2 t40 A096098 C1577 concat(A096098(n),n=1..182) A120716 C1101 * A037279^{4}(8) 4590@11e6 A130139 C364 * A037279^{6}(45) 17900@11e7 A130140 C36562 * A361320^{7}(15) 100@10000 A130141 C235 * A361580^{4}(35) 4590@11e6 A130142 C1437 * A361581^{5}(45) t15 A177876 C18701 * A003010(15) A177879 C4686 * A003010(13) A191648 C3840 * A130846^{4}(7) A195264 C178 * A195265(110) 17900@11e7, also needed by A195265 A330291 C195 concat(A330291(n),n=1..27)/22349 t45
Other sequences
id size description known ecm effort -------------------------------------------------------------------------------- A046461 C5497 * Sm(1651) 4590@11e6 A079560 C200 * A005150(19) 18340@11e7 also needed by A079562 A087552 C684 A065447(38) t47 A091335 C416 * Sylvester(11) 17900@11e7 also needed by A091336 A323605 C785 * Sylvester(12) t25 A101757 C288 * Tribonacci(1091) t48 A108728 C216 * A019520(91) t50 also needed by A105388 A109757 C414 * tens_complement_factorial(191)+1 4590@11e6 A109758 C183 * tens_complement_factorial(112)-1 t57 A113773 C285 * A008352(13) 4590@11e6 A153357 C207 A001008(476) t53 A177892 C540 * A003010(10) 17900@11e7 A249909 C310 * Euler(188) t45 A250295 C263 * A005165(150) 4480@11e6,1290@43e6 A110760 C205 * A007942(56) t55 also needed by A361624 A110759 C214 * A173426(59) t45 A110757 C179 A000422(107) t55 A113825 C371 * A008351(14) t52 A116087 C180 * A000041(A000045(24))
