an interesting problem

[Thomas Klemm]

(05-03-2015 03:10 AM)Paul Dale Wrote:  More realistically, by starting at the top of each list of six and stopping when we find a composite, we have to make fifteen primality checks.

By using the divisibilty rule by 7 we have to make 20 checks:

137 -1
173 11
317 17
371 35
713 65
731 71

139 -5
193 13
319 13
391 37
913 85
931 91

179 -1
197 5
719 53
791 77
917 77
971 95

379 19
397 25
739 55
793 73
937 79
973 91

But then the check needs only a little mental arithmetic.
By rearranging the numbers so that the first digit is last we have to make only 6 checks:

371 35
731 71
173 11
713 65
137 -1
317 17

391 37
931 91
193 13
913 85
139 -5
319 13

791 77
971 95
197 5
917 77
179 -1
719 53

793 73
973 91
397 25
937 79
379 19
739 55


Cheers
Thomas