- **Cunningham Tables**
(*https://www.mersenneforum.org/forumdisplay.php?f=51*)

- - **6+ table**
(*https://www.mersenneforum.org/showthread.php?t=3576*)

6+ table[code]Size Base Index Mod Diff Ratio
261 6 419 + 326 0.798 246 6 421 + 327.6 0.749 331 6 431 + 335.3 0.985 258 6 436 + 339.2 0.758 270 6 439 + 341.6 0.788 282 6 443 + 344.7 0.816 289 6 448 + 298.8 0.965 /7/resvd 283 6 449 + 349.3 0.807 311 6 454 + 353.2 0.878 344 6 457 + 355.6 0.965 336 6 458 + 356.3 0.941 280 6 461 + 358.7 0.8 327 6 463 + 360.2 0.906 311 6 464 + 361 0.859 320 6 466 + 362.6 0.881 312 6 472 + 367.2 0.848 281 6 473 + 334.6 0.838 /11q 338 6 478 + 371.9 0.907 309 6 479 + 372.7 0.827 337 6 481 + 345.4 0.973 /13 268 6 482 + 375 0.713 307 6 484 + 342.3 0.895 /11q 282 6 488 + 379.7 0.741 330 6 493 + 383.6 0.858 316 6 494 + 354.8 0.889 /13 315 6 496 + 385.9 0.814 258 6 497 + 331.4 0.776 /7 294 6 499 + 388.2 0.75 [/code] |

GMP-ECM 6.0.1 curves run on 6,762M (with default B2):
4362 curves with B1 = 11e6 6791 curves with B1 = 43e6 15504 curves with B1 = 11e7 -Jon |

6,363+ C172 = P75.P98
P75=103373476033477388263515282957106895317857131511194597652434632687520479231 This was done with ggnfs-0.77.1 using polynomial 36x^6-6x^3+1, 28 bit large primes, and algebraic/rational factor base limits of 14.8/16 million. |

6,287+ C154 = P66.P88
P66=247859037729470996906245243451923112548845447499779115951590660463 This was by SNFS (difficulty 191.4) with ggnfs-0.77.1, using polynomial x^6-x^5+x^4-x^3+x^2-x+1, 28 bit large primes, and algebraic/rational factor base limits of 14.7/20 million. Sieving took 66 GHz days on a mix of P2,P3,P4 CPUs, linear algebra took 10 GHz days on a P4, peak RAM usage was 714 MB. |

6,798L C140 = P57 * P84
P57 = 286227504202337752215096844369178117421662207554962805489 This was by GNFS with ggnfs CVS 20060310 using 28 bit large primes and algebraic/rational factor base limits of 14.1/14.0 million. Polynomial search took 9 GHz days on a P4/Celeron, sieving took 93 GHz days on a mix of P2,P3,P4 CPUs, linear algebra (on the third attempt) took 11 GHz days on a P4. Peak RAM usage was about 850 MB. |

factorization of 6^369+1The factorization of 6^369+1
[CODE]N=1995318523583569410536518710238825992069432091418126270747301312022729565418312904399527685768670754705838744041545211857263269211105325133582097428175392915125238452242062431167 ( 178 digits) SNFS difficulty: 191 digits. Divisors found: r1=13962920965423422985070859383439633233088296131740062300197159 (pp62) r2=142901225934358910616458334546032475881108357631878872140161426564856550164076857572859982163043154061736815224575913 (pp117)[/CODE] |

[QUOTE=smh;92575]The factorization of 6^369+1
[CODE]N=1995318523583569410536518710238825992069432091418126270747301312022729565418312904399527685768670754705838744041545211857263269211105325133582097428175392915125238452242062431167 ( 178 digits) SNFS difficulty: 191 digits. Divisors found: r1=13962920965423422985070859383439633233088296131740062300197159 (pp62) r2=142901225934358910616458334546032475881108357631878872140161426564856550164076857572859982163043154061736815224575913 (pp117)[/CODE][/QUOTE] Nice one. Sam's news letter arrived here this morning. Not sure whether you've received yours yet. Paul |

[QUOTE=xilman;92607]Sam's news letter arrived here this morning. Not sure whether you've received yours yet.[/QUOTE]Only a confirmation that he recieved the factors.
I guess i have to ask prof. Wagstaff to be included in this mailing list? |

156=53+103[QUOTE=garo;48285][CODE]Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal
... 6 337+ C156 0(2.63512) 2160(0.477957) 0(0.0754361) 300(0.0068697) 607055099444498921847583147982450809557514004451282871917948174791099265283291964431544302627498111551020109672026017537034605137651109768044489243175210279 ... [/CODE][/QUOTE] Not sure that I can give entirely satisfactory reasons, but the Opterons with first limit 110M (p55-optimal) are running circles around the xp's and the P3's (and another 80-some xeons that went idle), all with first limit 43M (p50-optimal). Score: 5-to-2. My intended reason was that c155-c169's tested to p50 were more likely to factor than the c234-c299 (as well as some time in c3xx), even though the latter were only tested to p45. With explanation that too many of the c234-c366's with factors under p45 removed had (on average) few factors in ecm range (like lots with smallest factor above p100, say). The first step limits oughtn't to make that much difference, as the factors being found are well within range of the smaller limits, given a larger number of curves. I'm fairly certain that the xp's are spending considerably more "work units" (without actually checking how these are actually defined); and with the addition on the xeons there's now a fairly substantial effort on the c155-c169's of difficulty under 220, that hasn't found anything at all (this year). Perhaps that's since smaller difficulty numbers had more ecm (from other users?), or the previous runs used smaller limits, so were less likely to miss p46-p54 factors (smaller standard deviation?). Anyway, here's the new one, p53=84382257093351217403808536729720911956398743537658819 with snfs difficulty 262.24, way harder than the 156-digit gnfs. -Bruce |

New Cunningham C122 (from 6,365+ after p60)[QUOTE=garo;48287][code]Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal
... 6 365+ C182 0(2.09174) 1500(0.38003) 590(0.0622008) 0(0.00529647) 18277199064023868716464418337366764898392423901374182657841980711016975079192366008607903315073044637550970940888219527035615248207222941096199986090387235389044400550718035078208621 ... [/code][/QUOTE] Another Opteron factor from the c170-c189's of difficulty 220 and up. One of the good points about this range is that any factor is likely to be useful. In this case, even the relatively low snfs difficulty 227 is way-harder than the cofactor: p60 = 254856004505238557834753259615355816338030694854500477132141 from c182, leaving a c122. I haven't heard yet from the usual suspects, but anyone considering polishing off the cofactor (please!) should make sure that they have a reservation with Sam before starting. -Bruce PS - this was from the 2nd Opteron pass, which has since finished on the c182/c122. So it's at 1.66*t50, ready for gnfs (presumably). [2*t50, actually] |

Your p60 isn't prime,
54856004505238557834753259615355816338030694854500477132141 = 3 * 32827965463229429509624429 * 557004815164707788478198263318443 nor do any of the two larger prime factors divide a Cunningham number. Cut-and-paste error? Alex |

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