Low weight k's
[center][size=+2]Low weight k's[/size][/center]
Please post here your results for low weight k's. In the Riesel Prime Database all low weight k's are colored in light blue (see the page 'Definitions' in the Data Section menu). All k's with Nash weight < 1000 are displayed so. Tools for calculating the Nash weight were done by T.Ritschel and can be found [url=http://www.mersenneforum.org/showthread.php?t=7213]here[/url]. 
Here we go; completion of all k's in the k=600K1.4M range that show with ZERO primes on rieselprime.org:
Lowweight k's searched to n=100K with primes found: [code] k: n's prime 491955: 45, 90, 355, 783, 2655, 4663, 8604, 9324, 9823, 13453, 16605, 16974, 17895, 27903 643843: 35 648433: 75 689909: 12, 24, 52, 240, 1116, 2504, 11676, 18000, 28376, 54644 1005449: 204, 41100 1006469: 61356 1011371: 246 1034503: 43, 5971 1180391: 17070, 40230 1210421: 28674 1230877: 6741, 12453 1234949: 676 1283759: 212, 1580 1310437: 20565 1343021: 50, 3170, 89138 [/code] Lowweight k's searched to n=300K with or without primes found: [code] 1005671: 120270 1049917*: (none) [/code] *Shown previously as searched to n=1M by someone else so is now officially doublechecked to n=300K. This leaves the following k's for k=600K1.4M with zero primes up to n=300K as tested previously and with this effort: 612509 671413 685183 686711 700057 780427 844559 963643 981493 1049917 Highweight 15 k's shown with zero primes at rieselprime.org are in the next post. (>new thread kar_bon) Gary 
91350658511197*2^n1 has no primes up to 1M

K=1019 searcehed to 1M  8, 48, 360, 1688, 2120, 2448, 4872, 32016, 484704

k=1087 searched to 1m  25, 73, 97, 1777, 22333, 81973

k=3221 searched to 1M  478, 3070, 7990, 29926, 102946

k=3313 searched to 1M  15, 103, 175, 655, 4743, 928263

k=3761 searched to 1M  810, 9474

K=1207 searched to 1M  61, 265, 10681, 24093, 52353, 106533, 163069, 261625, 269989

Partial "old" list
403 searched to 1M  981831 2039 searched to 1M  841312 2171 searched to 1M  no new primes 2279 searched to 1M  no new primes 2591 searched 333k to 1M  no new primes 2741 searched to 1M  50, 138, 1610, 1850, 3954, 10202, 23178, 84858, 468594, 737586 2759 searched to 1M  388, 405820, 569812 2797 searched to 1M  no new primes 2983 searched to 1M  11, 671, 767, 2891, 771455 3389 searched to 1M  92, 848, 2684,23864, 209996, 504584, 749828 3539 searched to 1M  12, 192, 4236, 869868 3821 searched to 1M  70, 15814, 439006 3823 searched 333k to 1M  7, 287, 335, 599, 1015, 2407,...384223 4001 searched to 1M  no new primes 4327 searched to 1M  no new primes 4597 searched to 1M  37, 161, 221, 721, 112009, 799781 5099 searched to 1M  184, 1216, 9936, 19072, 27648 5323 searched to 1M  27, 83, 8651, 107643 7331 searched to 1M  no new primes 9179 searched to 1M  no new primes 9613 searched to 1M  no new primes 10949 searched to 1M  no new primes 17077 searched to 1M  no new primes 19919 searched to 1M  no new primes 21547 searched to 1M  121, 2233, 16001, 310625, 936473 22183 searched to 1M  no new primes 24067 searched to 1M  no new primes 24671 searched to 1M  1290, 2250, 11698, 108906, 382066 25229 searched 325k to 1M  no new primes 30727 searched to 1M  no new primes 70079 searched 176k to 1M  no new primes 106303 searched 127k to 1M  no new primes 114613 searched to 1M  no new primes 117037 searched to 1M  no new primes 124679 searched to 1M  497244, 769908 132217 searched to 1M  no new primes 171607 searched to 1M  no new primes 179743 searched to 1M  no new primes 192509 searched to 1M  no new primes if a starting range is not stated, then I started from n=0 More later.. (kar_bon: "11025 searched to 1M  no new primes" deleted, because not correct) 
k=1183 searched to 1M  88683 < one new prime found
@ kar_bon 11025 has not been searched to 1M, my mistake :redface: 
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