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-   -   Low weight k's (https://www.mersenneforum.org/showthread.php?t=11053)

 kar_bon 2008-11-28 12:09

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].

 gd_barnes 2008-11-28 12:17

Here we go; completion of all k's in the k=600K-1.4M range that show with ZERO primes on rieselprime.org:

Low-weight 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]

Low-weight 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 double-checked to n=300K.

This leaves the following k's for k=600K-1.4M with zero primes up to n=300K as tested previously and with this effort:

612509
671413
685183
686711
700057
780427
844559
963643
981493
1049917

High-weight 15 k's shown with zero primes at rieselprime.org are in the next post. (->new thread kar_bon)

Gary

 henryzz 2008-11-29 19:07

91350658511197*2^n-1 has no primes up to 1M

 Beyond 2008-12-03 03:06

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

 Beyond 2008-12-04 22:47

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

 Beyond 2008-12-07 04:18

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

 Beyond 2008-12-09 03:34

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

 Beyond 2008-12-10 21:57

k=3761 searched to 1M - 810, 9474

 Beyond 2008-12-13 01:47

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

 Beyond 2008-12-14 17:12

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)

 Beyond 2008-12-17 10:39

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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