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Home > Numbers > Sequences
Some sums (Posted on 2012-03-26) Difficulty: 3 of 5
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.

See The Solution Submitted by Ady TZIDON    
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Solution solution | Comment 1 of 3

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 2012-03-26 09:53:38
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