13 Apr
2004
13 Apr
'04
3:39 p.m.
Let the nth Euclid number E_n be defined as 1 + (p_1 * ... * p_n) (aka 1 + the nth "primorial"), where p_n is the nth prime number. Neil Sloane's EIS sequence A006862 lists the first few n for which E_n is prime: 1,2,3,4,5,11,75,171,172,384,457,616,643,.... Some questions: 1. Are there infinitely many prime (resp. composite) E_n ??? 2. Is there a nice asymptotic expression for the number of E_n < x ??? 3. Same for prime (resp. composite) E_n ??? --Dan Daniel Asimov Visiting Scholar Mathematics Department University of California Berkeley, California