# # Numbers of shape: 41^(2^10) + b^(2^10) with 1 <= b < 41 # Filename: http://www.AlfredReich.com/GF.41.10.txt # Editor: Alfred Reich (zehnp@gmx.de) # Date: November 11, 2011 # Contributors: Kurt Beschorner and Alfred Reich # Status: 37 composites # # Notes: There are 40 numbers, each number has 1652 digits. # # Numbers of shape a^(2^m) + b^(2^m) with 1 <= b < a and gcd(a,b) = 1 are called Generalized Fermat Numbers and denoted by GF(a,b,m), # compare Hans Riesel, Prime Numbers and Computer Methods for Factorizations, 1994, 2nd ed, Birkhäuser, pp102 # and Wilfrid Keller, http://www.rrz.uni-hamburg.de/RRZ/W.Keller/GFNfacs.html. # # Contributions: b= 2: 1045674892646401 (Beschorner, Feb 10, 2011) # b= 2: 269360704990341121 (Beschorner, Feb 10, 2011) # b= 2: 197360372678819332097 (Beschorner, Feb 10, 2011) # b= 6: 117908008146033725082551058433 (Beschorner, Nov 14, 2011) (GMP-ECM, B1=1e6, sigma=1210092078) # b= 9: 4354170729222911805993827414017 (Beschorner, Nov 14, 2011) (GMP-ECM, B1=1e6, sigma=3242427810) # b= 9: 84105476841627998439563564474369 (Beschorner, Nov 14, 2011) (GMP-ECM, B1=1e6, sigma=15684811) # b= 9: 4742205410252951082493480050784567297 (Beschorner, Nov 14, 2011) (GMP-ECM, B1=1e6, sigma=713448171) # b=18: 174396492484399132247918593 (Beschorner, Oct 16, 2011) # b=18: 4022240400905726694802968577 (Beschorner, Oct 16, 2011) # b=21: 485365445595142482257116917761 (Beschorner, Oct 10, 2011) # b=25: 5821584645643916514299369269249 (Beschorner, Oct 9, 2011) # b=32: 54993538278135763190284503041 (Beschorner, Aug 9, 2011) # b=35: 22281835263871555557708907544424449 (Beschorner, Jul 5, 2011) # b=37: 10189737705814807237451177687971841 (Beschorner, Jun 23, 2011) # 1 2 133121 c1647 2 242307073 1045674892646401 269360704990341121 197360372678819332097 c1591 3 2 59393 c1647 4 1762885633 c1643 5 2 464897 3712664068097 71989911838721 c1620 6 311285761 1197408757512193 926687142075998209 1298724066070818212371273729 117908008146033725082551058433 p1554 7 2 18433 105152513 320801689391859185203201 c1616 8 22536193 37306369 13090018957313 2806798895410036657416193 p1600 9 2 524357633 37461943180646401 4354170729222911805993827414017 84105476841627998439563564474369 4742205410252951082493480050784567297 c1527 10 6952961 8460414547969 c1632 11 2 5222401 17799169 c1638 12 17360897 261777409 696388600553390081 492884106621578895361 p1598 13 2 1246025833592833 356122949032271873 569636788257951183403009 764157864864471263776769 c1571 14 c1652 15 2 6372096212966977573582849 637358655383489535602237441 c1600 16 18433 40961 163841 1492993 c1632 17 2 301057 285587152376679190259713 50236090487902929621727592449 c1594 18 3105110865964296345601 174396492484399132247918593 340981257233292981736744961 4022240400905726694802968577 c1550 19 2 35727361 c1644 20 354875393 124187811841 85809769494529 c1618 21 2 673793 1732609 246100314113 4812624308282011649 485365445595142482257116917761 c1580 22 2492417 c1646 23 2 1198081 341607036929 c1634 24 6873089 201715808257 c1634 25 2 18433 40961 41754171688961 942962135345842900993 5821584645643916514299369269249 c1577 26 18433 1008695408641 c1636 27 2 59393 5625857 c1640 28 c1652 29 2 163841 c1646 30 1171831412737 3098999542085210757121 c1618 31 2 65537 270337 196016129 c1633 32 131860481 1860526225638202316801 54993538278135763190284503041 c1594 33 2 61733167460353 c1638 34 9308161 c1645 35 2 120833 70490113 529563025795073 22281835263871555557708907544424449 c1590 36 c1652 37 2 18433 59393 9130462592540265076688897 10189737705814807237451177687971841 c1584 38 9023489 21347469709063739393 c1626 39 2 c1652 40 26787571634177 34082767157249 c1625