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2021-06-11, 16:21   #133
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

5·7·89 Posts

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)
Attached Files
 unsolved.zip (19.5 KB, 67 views)

 2021-08-06, 03:43 #134 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 C2B16 Posts (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
 2021-09-28, 07:04 #135 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 311510 Posts 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)
 2021-11-28, 15:12 #136 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 5·7·89 Posts 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.
 2021-11-28, 19:42 #137 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 1100001010112 Posts 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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