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Old 2021-02-18, 11:42   #144
sweety439
 
Nov 2016

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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)
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File Type: txt solved minimal prime set.txt (2.6 KB, 24 views)

Last fiddled with by sweety439 on 2021-02-19 at 19:55
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Old 2021-02-18, 11:46   #145
sweety439
 
Nov 2016

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Update the file of the condensed table (the current status for bases 2<=b<=16)
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File Type: txt condensed table for minimal primes in bases up to 16.txt (635 Bytes, 14 views)

Last fiddled with by sweety439 on 2021-02-19 at 19:32
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Old 2021-02-18, 15:31   #146
VBCurtis
 
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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.
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Old 2021-02-18, 15:42   #147
sweety439
 
Nov 2016

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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 109313)
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 3161)
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 42207)
b=8, d=5: 14 (the prime 51325)
b=8, d=6: 2 (the primes 661 and 667)
b=8, d=7: 12 (the prime 7121)
b=9, d=0: 1158 (the prime 30115811)
b=9, d=1: 36 (the prime 56136)
b=9, d=2: 4 (the prime 22227)
b=9, d=3: 8 (the prime 8333333335)
b=9, d=4: 11 (the prime 5411)
b=9, d=5: 4 (the prime 55551)
b=9, d=6: 329 (the prime 763292)
b=9, d=7: 687 (the prime 2768607)
b=9, d=8: 19 (the prime 819335)
b=10, d=0: 28 (the prime 502827)
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 5111)
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 403977)
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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