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A326609 Largest minimal prime in base n (written in base 10). 1
3, 13, 5, 3121, 5209, 2801, 76695841, 811, 66600049, 29156193474041220857161146715104735751776055777, 388177921 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(13) is (probably) 13^32020*8+183, it has 35670 digits, a(14) = 14^85*4+65, it has 99 digits, a(15) = (15^106*66-619)/7, it has 126 digits, a(16) = 16^3544*9+145, it has 4269 digits.

a(17) is the smallest prime of the form (4105*17^k-9)/16 if exists, otherwise (probably) (73*17^111333-9)/16 (136991 digits), a(18) = 18^31*304+1 (42 digits).

Other known terms: a(20) = (20^449*16-2809)/19 (585 digits), a(22) = 22^763*20+7041 (1026 digits), a(23) is (probably) (23^800873*106-7)/11 (1090573 digits), a(24) = (24^99*512-121)/23 (138 digits), a(30) = 30^1023*12+1 (1513 digits), a(42) = (42^487*27-1093)/41 (791 digits).

a(19) is the smallest prime of the form (15964*19^k-1)/3 if exists, otherwise (probably) (904*19^110984-1)/3 (141924 digits), a(21) is the smallest prime of the form 16*21^k+335 if exists, otherwise (probably) (51*21^479149-1243)/4 (633542 digits).

LINKS

Richard N. Smith, Table of n, a(n) for n = 2..16

Curtis Bright, Raymond Devillers, and Jeffrey Shallit, Minimal Elements for the Prime Numbers, preprint, 2014.

Curtis Bright, Raymond Devillers, and Jeffrey Shallit, Minimal Elements for the Prime Numbers, Experimental Mathematics, Volume 25, 2016 - Issue 3.

C. K. Caldwell, The Prime Glossary, minimal prime

Richard N. Smith, List of all known terms

Top PRPs, Search for 8*13^n+183

Top PRPs, Search for (73*17^n-9)/16

Top PRPs, Search for (106*23^n-7)/11

Wikipedia, Minimal prime (recreational mathematics)

CROSSREFS

Cf. A071062 (base 10 minimal primes), A110600 (base 12 minimal primes).

Cf. A293142 (largest non-repunit permutable prime), A317689 (largest non-repunit circular prime), A103443 (largest left-truncatable prime), A023107 (largest right-truncatable prime), A323137 (largest two-sided prime), A084738 (smallest repunit prime), A186995 (smallest weakly prime).

Sequence in context: A331806 A084738 A073580 * A230362 A173203 A140445

Adjacent sequences:  A326606 A326607 A326608 * A326610 A326611 A326612

KEYWORD

nonn,base,hard

AUTHOR

Richard N. Smith, Jul 13 2019

STATUS

approved

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Last modified April 5 03:58 EDT 2020. Contains 333238 sequences. (Running on oeis4.)