[seqfan] Re: Smallest prime with a substring of exactly n zeros

[Hans Havermann]

Nice. Next candidates are n=43 which would end with 301; n=46, with 501; and n=49, with 601. For n=50 the "1(n-1 zeros)a0b" form is not realized in primes. Can we just shift zeros into the a-b slot and still get the optimum answer? If so, n=50 would end (I think) with 500007.

> On Feb 19, 2016, at 11:18 AM, israel at math.ubc.ca wrote:
> 
> If all the numbers of the form a(n zeros)b and 1(n zeros)ab are all non-prime: a=1 to 9, b = 1,3,7,9, then the smallest prime with exactly n zeros is most likely to be of the form 1(n-1 zeros)a0b. The first time that happens is n=32, where if I haven't made a mistake A037053(32) = 10000000000000000000000000000000603.