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2018-12-11, 17:47   #7
CRGreathouse

Aug 2006

3×1,987 Posts

Quote:
 Originally Posted by enzocreti 2,3,4,7,8,12,19,22,36,46,51,67,79,215,359,394,451,1323,2131,3336,3371,6231,19179=9*2131,39699,51456,56238,69660,75894,79798,92020,174968, 176006,181015,285019,331259,360787,366770,...,541456
Quote:
 Originally Posted by enzocreti also this is a coincidence: pg(2131) is prime and pg(2131*9) is prime!!!
I think you might be on to something.

pg(36) is prime, and so is pg(36*1935).
pg(67) is prime, and so is pg(67*93).
pg(67) is prime, and so is pg(67*768).
pg(215) is prime, and so is pg(215*324).
pg(215) is prime, and so is pg(215*428).

I discarded the numbers under 36 (to avoid getting easy small multiples) and 541456 (because it wasn't clear if some numbers were skipped). This is far more than the number of multiples expected by chance.

Does this suggest that multiples of earlier terms are more likely, or just that having small factors are more likely? It's not clear to me.

Last fiddled with by CRGreathouse on 2018-12-11 at 17:57