Primes in Decimal Expansions

[J F]

Originally Posted by CRGreathouse

If you think that the number is actually normal, but you only know finitely many digits, I'd recommend the chi-squared statistic. If you think it's not normal, then you think there's some k and some k-digit string which appears with a frequency other than 1/b^k; I'd pick the smallest k and one of the strings maximizing the distance from the expected frequency and measure that.

Thanks!

Originally Posted by davar55

Since no one seems to want to work this problem...

Well, grab pixsieve and pfgw, and there you go.

[rogue]

Originally Posted by CRGreathouse

http://mathworld.wolfram.com/ConstantPrimes.html
has a nice summary table, you could see if there are differences between the (known) algebraic numbers and the others. It's a little hard to do analysis because not that many terms are known -- it's hard to test big numbers for primality.

FYI, the current search limit for some of these can be found here.

[Batalov]

Some of the limits are quite dated, though.
E.g. take Irregular primes ... http://primes.utm.edu/top20/page.php?id=26
Note added after looking in PRPtop: ...and both lists are behind on the largest known Irregular PRP, anyway; it is dated 06/2017.

So it is for sure a good starting point but in any particular case more search is usually needed. UTM, OEIS, primeform discussion group...