8645 is a very interesting number. It's the largest known n such that the menage number M(n) is prime*: https://oeis.org/A249394 So far the sequence is {4, 5, 13, 53, 8645}, and Hans Havermann has exhausted up to 28000 (possibly further?) without finding any more. Heuristically, we expect this sequence to grow doubly exponentially, and thus for the menage primes themselves to grow triply-exponentially. Which might mean we never find another. * according to PrimeQ. We might want to generate a certificate for its primality to be on the safe side. Best wishes, Adam P. Goucher

Sent: Thursday, November 29, 2018 at 2:27 AM From: "Bill Gosper" <billgosper@gmail.com> To: math-fun@mailman.xmission.com Subject: [math-fun] It would take five Ramanujans to impeach Trump

In[845]:= 5*1729

Out[845]= 8645 —rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun