[jiekvsvp] Frobeniusly strong Lucas pseudoprimes

We compute composites (pseudoprimes) which pass the strong Lucas primality test with P and Q chosen by Selfridge Method A, and additionally satisfy the Frobenius-like criterion V[n+1] = 2Q (mod n) mentioned in Baillie's original paper, which can be tested almost for free.

There are 304 such pseudoprimes less than 10^9, and 757 less than 10^10.  The corresponding numbers for the strong Lucas pseudoprime test without the above Frobenius-like criterion are 1415 and 3622, so this almost-free test improves things significantly. (See OEIS A217255 and http://ntheory.org/pseudoprimes.html). These Frobeniusly strong Lucas pseudoprimes are a subset of the strong Lucas pseudoprimes.

Below are the 304 pseudoprimes less than 10^9.  Further pseudoprimes here.  Source code will be posted later.

5777 10877 75077 100127 113573 161027 162133 231703 430127 635627 851927 1033997 1106327 1256293 1388903 1697183 2263127 2435423 2662277 3175883 3399527 3452147 3774377 3900797 4109363 4226777 4403027 4828277 4870847 5208377 5942627 6003923 7353917 8518127 9401893 9713027 9793313 9922337 10054043 11637583 13277423 13455077 13695947 14015843 14985833 15754007 16485493 16685003 17497127 19168477 19347173 20018627 22361327 23307377 24157817 25948187 27854147 29395277 29604893 30299333 31622993 31673333 32702723 33816593 34134407 34175777 36061997 39240233 39247393 39850127 40928627 41177993 42389027 42525773 47297543 49219673 49476377 50075027 51931333 53697953 57464207 59268827 62133377 64610027 67081607 67237883 69244097 70894277 73295777 73780877 74580767 75239513 75245777 75983627 83241013 83963177 85015493 85903277 86023943 87471017 89746073 90686777 91418543 93400277 98385377 100981997 104943827 106728053 110734667 116853827 117772877 122879063 124477513 131017577 131990627 136579127 139904627 140782823 142593827 143221993 144967877 146278373 148472347 150204577 153256277 154308527 156715343 157132127 158197577 163578827 166850777 168018353 171579883 177991277 179295443 184135673 185504633 186003827 192227027 196754513 202368143 207023087 210089303 211099877 213361937 226525883 229206347 231437957 247030877 247882963 253755053 254194877 257339503 257815277 259179527 264250367 264689963 276795217 277932113 280075277 284828777 290256947 293485877 306219377 311387693 312189697 316701527 320234777 320297657 334046627 344107133 347522647 347547437 360783793 370020797 375578683 376682627 384646597 386628527 387009737 400091327 400657277 401790377 403675973 409245563 420717527 429992597 432988877 437118527 438894377 439744397 440964593 443146057 443969063 448504697 450825377 455039027 456780193 461700077 461807147 461819483 464407883 465523103 465964127 467486627 468245207 469721647 475167377 480053573 480891143 481033907 485326403 495101777 500337713 504097397 523827527 540136277 543893783 544339637 546540347 552576653 558030527 562046627 563601257 570122027 574181327 577647017 582182327 582934477 583031693 584238563 590901317 595402877 598147577 598364773 623709217 628919117 634888253 638227127 640151777 649354103 657333797 657665777 659936423 664939277 667595897 670042903 670786877 672810497 686258627 688773443 691455077 691593047 692726473 704907377 706840573 709706567 713971187 721652587 727615877 729645563 731349233 734498627 747587777 756310507 768614027 771325967 772719947 773515133 780421277 788342777 797102627 798790787 799500077 800484227 807775547 811541327 812957903 825393997 831065633 838472417 839350363 847053323 847887823 856901267 863097377 869420473 873933527 878330573 922483693 923962577 930039743 940801877 947756267 957697997 961095923 961931213 969210377 978920627 979805777 983720077 985125077 986079553 988367813