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Old 2021-06-11, 16:21   #133
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

5·7·89 Posts
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Done for all bases <=50

Bases 43, 47, 49 are not listed as they have some unsolved families x{y}z with |x|>=7 or |z|>=7, thus my excel program cannot handle (will give error a or c value for (a*b^n+c)/d)
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File Type: zip unsolved.zip (19.5 KB, 67 views)
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Old 2021-08-06, 03:43   #134
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

C2B16 Posts
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(Probable) primes found for base 31:

Code:
E8(U^21866)P = 443*31^21867-6
IE(L^29787) = (5727*31^29787-7)/10
L(F^21052)G = (43*31^21053+1)/2
MI(O^10747)L = (3504*31^10748-19)/5
PEO(0^22367)Q = 24483*31^22368+26
(R^22137)1R = (9*31^22139-8069)/10
Unsolved families searched to high depth with no (probable) prime found:

Code:
ILE(L^n) = (179637*31^n-7)/10 at n=30000 (now unneeded since IE(L^29787) is (probable) prime)
L0(F^n)G = (1303*31^(n+1)+1)/2 at n=23000 (now unneeded since L(F^21052)G is (probable) prime)
M(P^n) = (137*31^n-5)/6 at n=39000
P(F^n)G = (51*31^(n+1)+1)/2 at n=32000
(R^n)1 = (9*31^(n+1)-269)/10 at n=20000
(R^n)8 = (9*31^(n+1)-199)/10 at n=19000
(U^n)P8K = 31^(n+3)-5498 at n=27000
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Old 2021-09-28, 07:04   #135
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

311510 Posts
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Newest status for the unsolved families in base 31:

(probable) primes found:

Code:
E8{U}P: prime at length 21869 (the prime is 443*31^21867-6)
IE{L}: prime at length 29789 (the prime is (5727*31^29787-7)/10)
L{F}G: prime at length 21054 (the prime is (43*31^21053+1)/2)
MI{O}L: prime at length 10750 (the prime is (3504*31^10748-19)/5)
PEO{0}Q: prime at length 22371 (the prime is 24483*31^22368+26)
{L}9G: prime at length 10014 (the prime is (6727*31^10012-3777)/10)
{R}1R: prime at length 22139 (the prime is (9*31^22139-8069)/10)
unneeded families:

Code:
ILE{L} (tested to length 30000, but IE{L} has prime at length 29789)
L0{F}G (tested to length 23000, but L{F}G has prime at length 21054)
{L}9IG (tested to length 13000, but {L}9G has prime at length 10014)
unsolved families:

Code:
M{P} (at length 39000) (the formula is (137*31^n-5)/6)
P{F}G (at length 32000) (the formula is (1581*31^n+1)/2)
SP{0}K (at length 28000) (the formula is 27683*31^n+20)
{F}G (at length 4194303) (the formula is (31*31^n+1)/2)
{F}KO (the formula is (961*31^n+327)/2)
{F}RA (the formula is (961*31^n+733)/2)
{L}CE (at length 21000) (the formula is (6727*31^n-2867)/10)
{L}G (at length 30000) (the formula is (217*31^n-57)/10)
{L}IS (at length 25000) (the formula is (6727*31^n-867)/10)
{L}SO (at length 22000) (the formula is (6727*31^n+2193)/10)
{P}I (at length 32000) (the formula is (155*31^n-47)/6)
{R}1 (at length 27000) (the formula is (279*31^n-269)/10)
{R}8 (at length 33000) (the formula is (8649*31^n-8069)/10)
{U}P8K (at length 30000) (the formula is 29791*31^n-5498)
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Old 2021-11-28, 15:12   #136
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

5·7·89 Posts
Default

If 1 is regarded as prime, then all bases <=20 are solved, in fact, all bases <=24 except the base 21 family G{0}FK is solved.

Code:
b    largest minimal prime
2    1
3    2
4    3
5    3
6    5
7    5
8    7
9    7
10   946669
11   A999999999999999999999
12   B
13   940000000000000000000000000000000000C
14   40000000000000000000000000000000000000000000000000000000000000000000000000000000000049
15   96666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666608
16   F88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888F
17   4(9^111333)
18   H
19   FG(6^110984)
20   GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG99
21   ? (the smallest prime of the form G{0}FK if exists, otherwise C(F^479147)0K)
22   IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIAF
23   9(E^800873)
24   N
However, for base 25, there are 6 unsolved families:

Code:
6M{F}9
EF{O}
F{0}KO
F0{K}O
LO{L}8
O{L}8
besides, for bases in https://oeis.org/A048597, the largest minimal prime is the largest prime < base (i.e. the largest single-digit prime), since all digits coprime to the base are primes.
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Old 2021-11-28, 19:42   #137
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

1100001010112 Posts
Default

For the minimal set of "noncomposites" (i.e. 0, 1, primes), all bases <=24 are completely solved:

Code:
b    largest minimal noncomposite
2    1
3    2
4    3
5    3
6    5
7    5
8    7
9    7
10   946669
11   A999999999999999999999
12   B
13   9866666666666666666666666666
14   99999999999999999999999999999999999989
15   E9666666666666668
16   F88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888F
17   4(9^111333)
18   H
19   FG(6^110984)
20   GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG99
21   AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA6FK
22   IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIAF
23   9(E^800873)
24   N
and base 25 has 4 unsolved families:

Code:
6M{F}9
EF{O}
LO{L}8
O{L}8
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