A227775 Smallest prime that is a concatenation in base n of two or more successive numbers beginning with a power of n (including n^0=1).

11, 5, 1298074219469410275663133932519427, 7, 223, 131870666077, 83, 11

Offset: 2

Author

James G. Merickel, Jul 30 2013

Keywords

• nonn
• base

Comments

Terms computed by expanding the print for the program at A173189 (to include the variable r).

a(10) consists of 10^13 followed by 10^13+k, k=1 to 9 in order (140 digits), and then follow 13 and 1741. a(13) has 258 decimal digits, and then 227, 17, 320255973501901, 19 and 5851 follow before a P209 arises for n=19 (n=31 produces the next prime that would not fit a mainline sequence here, at 467 digits; and the number for n=67, the concatenation in that base of 67^19 through 67^19+525, is a whopping 19209 decimal digits). Terms through at least n=78 may be found in a reasonable time using the program (and sped up by a small factor if it is modified to only search for r). a(79) is very large, however, and has a high heuristic probability of being beyond current computational means, as candidates having the right number of numbers concatenated to avoid being divisible by a small prime arise only about once every 11 orders of magnitude.

Examples

			11 is the decimal representation of the value for n=2 as the concatenation 10 followed by 11 in binary, with the only smaller concatenation of type (110, 6 in decimal) composite.
		

Links

• Prime Curios!, 10000...00009 (140-digits)

Crossrefs

Cf. A173189.

Formula

a(p-2) = p if p is an odd prime.