I’m looking for an instance of a prime for numbers of the form (10^n 78880-1)/3, where n is a positive integer. As a preliminary, it may be noted that n must be a multiple of 12. There are many other constraints based on division by small factors but since PrimeQ has a built-in small-factor trial-division subroutine, ultimately I am interested in those n that escape that subroutine, i.e. n where PrimeQ[(10^n 78880-1)/3] takes more than a second or so to evaluate. For example, the numbers 10008, 10032, 10068, 10140, 10188, 10320, 10332, 10368, 10392, 10404, 10584, 10608, 10620, 10644, 10692, 10764, 10824, 10872, 10932, 10980, 11004, … I’d like to extend that list to, say, 10^6. How do I interrupt an evaluation that is taking too long so that I might move on to another candidate?
Pretty sure you just want TimeConstrained:
TimeConstrained[ code, limit]
That will return as $Aborted, but you can also return a different failure case with the 3rd argument:
TimeConstrained[Do[i^2, {i, 1000000}], 1, $Failed]
Yes. That worked, thank you! Can someone confirm that Mathematica 10 is significantly less astute at PrimeQ than Mathematica 9? Timing[PrimeQ[(10^9600 78880-1)/3]] yields {7.265538,False} in 10 and {0.003482,False} in 9 (on a four-year-old iMac running Yosemite). That strikes me as a bug.