2021-02-18, 11:42 | #144 |
Nov 2016
2^{2}×3×5×47 Posts |
Update the text file for solved minimal prime (start with b+1) set
(Note: the set of base 7 is only conjectured, I think this set is complete but I cannot prove it, and I tried to find more primes in this set (find simple families which have no primes in current set but not ruled out as only contain composites (only count numbers > base)) and with no success, thus I think that this set is complete) Last fiddled with by sweety439 on 2021-02-19 at 19:55 |
2021-02-18, 11:46 | #145 |
Nov 2016
2^{2}·3·5·47 Posts |
Update the file of the condensed table (the current status for bases 2<=b<=16)
Last fiddled with by sweety439 on 2021-02-19 at 19:32 |
2021-02-18, 15:31 | #146 |
"Curtis"
Feb 2005
Riverside, CA
3×1,579 Posts |
Your work does not rate daily posts to update us.
If you continue to post to this thread every single day, you're going to find yourself with time off again. Try monthly update posts. Yes, monthly. You can edit your previously posted attachments without triggering a new-post notice to all the mods- try that too. But if you keep drawing attention to your endless procession of trivial update posts, you're likely to lose the ability to make those posts. |
2021-02-18, 15:42 | #147 |
Nov 2016
5404_{8} Posts |
The largest possible appearance for given digit d in minimal prime (start with b+1) in base b: (note: the case for b=7 and b=9 are only conjectured (assume my sets for these bases are complete), not proven)
If base b has repunit primes, then the largest possible appearance for digit d=1 in minimal prime (start with b+1) in base b is the length of smallest repunit prime base b (i.e. A084740(b)), the first bases which do not have repunit primes are 9, 25, 32, 49, 64, ... Code:
b=2, d=0: 0 b=2, d=1: 2 (the prime 11) b=3, d=0: 0 b=3, d=1: 3 (the prime 111) b=3, d=2: 1 (the primes 12 and 21) b=4, d=0: 0 b=4, d=1: 2 (the prime 11) b=4, d=2: 2 (the prime 221) b=4, d=3: 1 (the primes 13, 23, 31) b=5, d=0: 93 (the prime 10_{93}13) b=5, d=1: 3 (the prime 111) b=5, d=2: 1 (the primes 12, 21, 23, 32) b=5, d=3: 4 (the prime 33331) b=5, d=4: 4 (the primes 14444 and 44441) b=6, d=0: 2 (the prime 40041) b=6, d=1: 2 (the prime 11) b=6, d=2: 1 (the primes 21 and 25) b=6, d=3: 1 (the primes 31 and 35) b=6, d=4: 3 (the prime 4441) b=6, d=5: 1 (the primes 15, 25, 35, 45, 51) b=7, d=0: 7 (the prime 5100000001) b=7, d=1: 5 (the prime 11111) b=7, d=2: 3 (the prime 1222) b=7, d=3: 16 (the prime 3_{16}1) b=7, d=4: 2 (the primes 344, 445, 544, 4504, 40054) b=7, d=5: 4 (the prime 35555) b=7, d=6: 2 (the prime 6634) b=8, d=0: 3 (the prime 500025) b=8, d=1: 3 (the prime 111) b=8, d=2: 2 (the prime 225) b=8, d=3: 3 (the prime 3331) b=8, d=4: 220 (the prime 4_{220}7) b=8, d=5: 14 (the prime 5_{13}25) b=8, d=6: 2 (the primes 661 and 667) b=8, d=7: 12 (the prime 7_{12}1) b=9, d=0: 1158 (the prime 30_{1158}11) b=9, d=1: 36 (the prime 561_{36}) b=9, d=2: 4 (the prime 22227) b=9, d=3: 8 (the prime 8333333335) b=9, d=4: 11 (the prime 54_{11}) b=9, d=5: 4 (the prime 55551) b=9, d=6: 329 (the prime 76_{329}2) b=9, d=7: 687 (the prime 27_{686}07) b=9, d=8: 19 (the prime 8_{19}335) b=10, d=0: 28 (the prime 50_{28}27) b=10, d=1: 2 (the prime 11) b=10, d=2: 3 (the prime 2221) b=10, d=3: 1 (the primes 13, 23, 31, 37, 43, 53, 73, 83, 349) b=10, d=4: 2 (the prime 449) b=10, d=5: 11 (the prime 5_{11}1) b=10, d=6: 4 (the prime 666649) b=10, d=7: 2 (the primes 277, 577, 727, 757, 787, 877) b=10, d=8: 2 (the prime 881) b=10, d=9: 3 (the prime 9949) b=12, d=0: 39 (the prime 40_{39}77) b=12, d=1: 2 (the prime 11) b=12, d=2: 3 (the prime 222B) b=12, d=3: 1 (the primes 31, 35, 37, 3B) b=12, d=4: 3 (the prime 4441) b=12, d=5: 2 (the primes 565 and 655) b=12, d=6: 2 (the prime 665) b=12, d=7: 3 (the primes 4777 and 9777) b=12, d=8: 1 (the primes 81, 85, 87, 8B) b=12, d=9: 4 (the prime 9999B) b=12, d=A: 4 (the prime AAAA1) b=12, d=B: 7 (the prime BBBBBB99B) Last fiddled with by sweety439 on 2021-02-19 at 07:58 |
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