The sum of k consecutive primes is a prime number.
List all the possibilties for k=2,3,5 and 7 with the sums under 300.
Given are the range of consecutive primes (p1:p2) followed by the total sum of these primes:
k = 2
(2 : 3) = 5
k = 3
(5 :11) = 23
(7 :13) = 31
(11:17) = 41
(17:23) = 59
(19:29) = 71
(23:31) = 83
(29:37) = 97
(31:41) = 109
(41:47) = 131
(53:61) = 173
(61:71) = 199
(67:73) = 211
(71:79) = 223
(79:89) = 251
(83:97) = 269
k = 5
(5 :17) = 53
(7 :19) = 67
(11:23) = 83
(13:29) = 101
(19:37) = 139
(29:43) = 181
(31:47) = 199
(43:61) = 263
k = 7
(17:41) = 197
(19:43) = 223
(23:47) = 251
(29:53) = 281
Additionally for sums of consecutive primes that total under 300 yet are primes, k may be 4, 6, 9, 11, 12 and 14.
k = 4
(2 : 7) = 17
k = 6
(2 :13) = 41
k = 9
(3 :29) = 127
k = 11
(5 :41) = 233
k = 12
(2 :37) = 197
k = 14
(2 :43) = 281

Posted by Dej Mar
on 20120326 09:53:38 