- Can anyone find a set of 37 consecutive odd positive primes, where one of these integers 1, 3, 7 and 9 is NOT present among the rightmost digits of the primes in the set? P091207-72

For every N from 4 to 36, I managed to find such a set of N primes. For example, in the set of N=36 primes starting with 5376557 and ending with 5377039, the rightmost digit 1 is not present. So far no luck with N=37.

I wonder if 36 is the limit, implying that in any set of 37 consecutive primes all 4 integers 1, 3, 7 and 9 are always present among the rightmost digits of the primes in the set ? Thanks folks.

Bill Sindelar

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[Non-text portions of this message have been removed] - Bill Sindelar wrote:
> Can anyone find a set of 37 consecutive odd positive primes,

Record runs above 36:

> where one of these integers 1, 3, 7 and 9 is NOT present

> among the rightmost digits of the primes in the set?

40 with no 9: 62024761 to 62025377

43 with no 3: 133125211 to 133126009

48 with no 1: 149054309 to 149055259

51 with no 1: 1206644317 to 1206645493

53 with no 9: 1770847261 to 1770848447

54 with no 3: 2343368669 to 2343370021

57 with no 3: 2462372461 to 2462373707

61 with no 9: 76047287171 to 76047288677

62 with no 7: 86722358543 to 86722360553

It seems highly likely there can be arbitrarily many.

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Jens Kruse Andersen