Prime Numbers | 4 Aug 2009

List a set of prime numbers where the sum total of the complete set is 100.

The sum of first 9 prime number is 100:

2
3
5
7
11
13
17
19
23

Well there are other possiblities too..but im just considering the first set n obviously the easier one to figure out... :P

97 and 3

The first (and smallest) set that I could think of immediately was 97+3.
But, your answer is acceptable too.
So, congrats

Thanks saswat

Listings all possible sets that I could think of

03 97
11 89
02 03 05 07 83
02 03 05 11 79
02 03 05 17 73
02 03 05 19 71
02 07 11 13 67
02 07 13 17 61
02 07 11 19 61
02 03 05 07 11 13 59
02 03 05 07 13 17 53
02 03 05 11 13 19 47
03 05 13 17 19 43
02 03 05 13 17 19 41
03 11 13 17 19 37
02 07 11 13 17 19 31
02 03 05 07 11 13 17 19 23
05 07 17 19 23 29
07 11 13 17 23 29

This are the first 9 prime numbers as well which when verifying yesterdays sum hit as 100. So formed this one.

Congrats rik

OK, now that I have coded my own super-fast generator, I would like to mention that this list is far from complete, the complete list has 233 different sets. The list is :

--> { 3, 97 }
--> { 11, 89 }
--> { 17, 83 }
--> { 29, 71 }
--> { 41, 59 }
--> { 47, 53 }
--> { 2, 19, 79 }
--> { 2, 31, 67 }
--> { 2, 37, 61 }
--> { 3, 5, 13, 79 }
--> { 3, 5, 19, 73 }
--> { 3, 5, 31, 61 }
--> { 3, 7, 11, 79 }
--> { 3, 7, 17, 73 }
--> { 3, 7, 19, 71 }
--> { 3, 7, 23, 67 }
--> { 3, 7, 29, 61 }
--> { 3, 7, 31, 59 }
--> { 3, 7, 37, 53 }
--> { 3, 7, 43, 47 }
--> { 3, 11, 13, 73 }
--> { 3, 11, 19, 67 }
--> { 3, 11, 43, 43 }
--> { 3, 13, 17, 67 }
--> { 3, 13, 23, 61 }
--> { 3, 13, 31, 53 }
--> { 3, 13, 37, 47 }
--> { 3, 13, 41, 43 }
--> { 3, 17, 19, 61 }
--> { 3, 17, 37, 43 }
--> { 3, 19, 31, 47 }
--> { 3, 19, 37, 41 }
--> { 3, 23, 31, 43 }
--> { 3, 23, 37, 37 }
--> { 3, 29, 31, 37 }
--> { 5, 7, 17, 71 }
--> { 5, 7, 29, 59 }
--> { 5, 7, 41, 47 }
--> { 5, 11, 13, 71 }
--> { 5, 11, 17, 67 }
--> { 5, 11, 23, 61 }
--> { 5, 11, 31, 53 }
--> { 5, 11, 37, 47 }
--> { 5, 11, 41, 43 }
--> { 5, 13, 23, 59 }
--> { 5, 13, 29, 53 }
--> { 5, 13, 41, 41 }
--> { 5, 17, 19, 59 }
--> { 5, 17, 31, 47 }
--> { 5, 17, 37, 41 }
--> { 5, 19, 23, 53 }
--> { 5, 19, 29, 47 }
--> { 5, 23, 29, 43 }
--> { 5, 23, 31, 41 }
--> { 7, 11, 23, 59 }
--> { 7, 11, 29, 53 }
--> { 7, 11, 41, 41 }
--> { 7, 13, 19, 61 }
--> { 7, 13, 37, 43 }
--> { 7, 17, 23, 53 }
--> { 7, 17, 29, 47 }
--> { 7, 19, 31, 43 }
--> { 7, 19, 37, 37 }
--> { 7, 23, 29, 41 }
--> { 11, 13, 17, 59 }
--> { 11, 13, 23, 53 }
--> { 11, 13, 29, 47 }
--> { 11, 17, 19, 53 }
--> { 11, 17, 29, 43 }
--> { 11, 17, 31, 41 }
--> { 11, 19, 23, 47 }
--> { 11, 19, 29, 41 }
--> { 11, 23, 29, 37 }
--> { 13, 17, 23, 47 }
--> { 13, 17, 29, 41 }
--> { 13, 19, 31, 37 }
--> { 17, 19, 23, 41 }
--> { 17, 23, 29, 31 }
--> { 19, 23, 29, 29 }
--> { 2, 3, 5, 7, 83 }
--> { 2, 3, 5, 11, 79 }
--> { 2, 3, 5, 17, 73 }
--> { 2, 3, 5, 19, 71 }
--> { 2, 3, 5, 23, 67 }
--> { 2, 3, 5, 29, 61 }
--> { 2, 3, 5, 31, 59 }
--> { 2, 3, 5, 37, 53 }
--> { 2, 3, 5, 43, 47 }
--> { 2, 3, 7, 17, 71 }
--> { 2, 3, 7, 29, 59 }
--> { 2, 3, 7, 41, 47 }
--> { 2, 3, 11, 13, 71 }
--> { 2, 3, 11, 17, 67 }
--> { 2, 3, 11, 23, 61 }
--> { 2, 3, 11, 31, 53 }
--> { 2, 3, 11, 37, 47 }
--> { 2, 3, 11, 41, 43 }
--> { 2, 3, 13, 23, 59 }
--> { 2, 3, 13, 29, 53 }
--> { 2, 3, 13, 41, 41 }
--> { 2, 3, 17, 19, 59 }
--> { 2, 3, 17, 31, 47 }
--> { 2, 3, 17, 37, 41 }
--> { 2, 3, 19, 23, 53 }
--> { 2, 3, 19, 29, 47 }
--> { 2, 3, 23, 29, 43 }
--> { 2, 3, 23, 31, 41 }
--> { 2, 5, 7, 13, 73 }
--> { 2, 5, 7, 19, 67 }
--> { 2, 5, 7, 43, 43 }
--> { 2, 5, 11, 23, 59 }
--> { 2, 5, 11, 29, 53 }
--> { 2, 5, 11, 41, 41 }
--> { 2, 5, 13, 19, 61 }
--> { 2, 5, 13, 37, 43 }
--> { 2, 5, 17, 23, 53 }
--> { 2, 5, 17, 29, 47 }
--> { 2, 5, 19, 31, 43 }
--> { 2, 5, 19, 37, 37 }
--> { 2, 5, 23, 29, 41 }
--> { 2, 7, 11, 13, 67 }
--> { 2, 7, 11, 19, 61 }
--> { 2, 7, 11, 37, 43 }
--> { 2, 7, 13, 17, 61 }
--> { 2, 7, 13, 19, 59 }
--> { 2, 7, 13, 31, 47 }
--> { 2, 7, 13, 37, 41 }
--> { 2, 7, 17, 31, 43 }
--> { 2, 7, 17, 37, 37 }
--> { 2, 7, 19, 29, 43 }
--> { 2, 7, 19, 31, 41 }
--> { 2, 7, 23, 31, 37 }
--> { 2, 7, 29, 31, 31 }
--> { 2, 11, 13, 31, 43 }
--> { 2, 11, 13, 37, 37 }
--> { 2, 11, 17, 23, 47 }
--> { 2, 11, 17, 29, 41 }
--> { 2, 11, 19, 31, 37 }
--> { 2, 13, 17, 31, 37 }
--> { 2, 13, 19, 23, 43 }
--> { 2, 13, 19, 29, 37 }
--> { 2, 13, 23, 31, 31 }
--> { 2, 17, 19, 31, 31 }
--> { 2, 17, 23, 29, 29 }
--> { 3, 5, 7, 11, 13, 61 }
--> { 3, 5, 7, 11, 31, 43 }
--> { 3, 5, 7, 11, 37, 37 }
--> { 3, 5, 7, 13, 19, 53 }
--> { 3, 5, 7, 13, 29, 43 }
--> { 3, 5, 7, 13, 31, 41 }
--> { 3, 5, 7, 17, 31, 37 }
--> { 3, 5, 7, 19, 23, 43 }
--> { 3, 5, 7, 19, 29, 37 }
--> { 3, 5, 7, 23, 31, 31 }
--> { 3, 5, 11, 13, 31, 37 }
--> { 3, 5, 11, 17, 23, 41 }
--> { 3, 5, 11, 19, 31, 31 }
--> { 3, 5, 11, 23, 29, 29 }
--> { 3, 5, 13, 17, 19, 43 }
--> { 3, 5, 13, 17, 31, 31 }
--> { 3, 5, 13, 19, 23, 37 }
--> { 3, 5, 13, 19, 29, 31 }
--> { 3, 7, 11, 13, 19, 47 }
--> { 3, 7, 11, 13, 23, 43 }
--> { 3, 7, 11, 13, 29, 37 }
--> { 3, 7, 11, 17, 19, 43 }
--> { 3, 7, 11, 17, 31, 31 }
--> { 3, 7, 11, 19, 23, 37 }
--> { 3, 7, 11, 19, 29, 31 }
--> { 3, 7, 13, 17, 19, 41 }
--> { 3, 7, 13, 17, 23, 37 }
--> { 3, 7, 13, 17, 29, 31 }
--> { 3, 7, 13, 19, 29, 29 }
--> { 3, 7, 17, 19, 23, 31 }
--> { 3, 11, 13, 17, 19, 37 }
--> { 3, 11, 13, 19, 23, 31 }
--> { 5, 7, 11, 13, 17, 47 }
--> { 5, 7, 11, 13, 23, 41 }
--> { 5, 7, 11, 17, 19, 41 }
--> { 5, 7, 11, 17, 23, 37 }
--> { 5, 7, 11, 17, 29, 31 }
--> { 5, 7, 11, 19, 29, 29 }
--> { 5, 7, 13, 17, 29, 29 }
--> { 5, 7, 17, 19, 23, 29 }
--> { 5, 11, 13, 17, 23, 31 }
--> { 5, 11, 13, 19, 23, 29 }
--> { 5, 13, 17, 19, 23, 23 }
--> { 7, 11, 13, 17, 23, 29 }
--> { 7, 11, 17, 19, 23, 23 }
--> { 2, 3, 5, 7, 11, 13, 59 }
--> { 2, 3, 5, 7, 11, 19, 53 }
--> { 2, 3, 5, 7, 11, 29, 43 }
--> { 2, 3, 5, 7, 11, 31, 41 }
--> { 2, 3, 5, 7, 13, 17, 53 }
--> { 2, 3, 5, 7, 13, 23, 47 }
--> { 2, 3, 5, 7, 13, 29, 41 }
--> { 2, 3, 5, 7, 17, 19, 47 }
--> { 2, 3, 5, 7, 17, 23, 43 }
--> { 2, 3, 5, 7, 17, 29, 37 }
--> { 2, 3, 5, 7, 19, 23, 41 }
--> { 2, 3, 5, 7, 23, 29, 31 }
--> { 2, 3, 5, 11, 13, 19, 47 }
--> { 2, 3, 5, 11, 13, 23, 43 }
--> { 2, 3, 5, 11, 13, 29, 37 }
--> { 2, 3, 5, 11, 17, 19, 43 }
--> { 2, 3, 5, 11, 17, 31, 31 }
--> { 2, 3, 5, 11, 19, 23, 37 }
--> { 2, 3, 5, 11, 19, 29, 31 }
--> { 2, 3, 5, 13, 17, 19, 41 }
--> { 2, 3, 5, 13, 17, 23, 37 }
--> { 2, 3, 5, 13, 17, 29, 31 }
--> { 2, 3, 5, 13, 19, 29, 29 }
--> { 2, 3, 5, 17, 19, 23, 31 }
--> { 2, 3, 7, 11, 13, 17, 47 }
--> { 2, 3, 7, 11, 13, 23, 41 }
--> { 2, 3, 7, 11, 17, 19, 41 }
--> { 2, 3, 7, 11, 17, 23, 37 }
--> { 2, 3, 7, 11, 17, 29, 31 }
--> { 2, 3, 7, 11, 19, 29, 29 }
--> { 2, 3, 7, 13, 17, 29, 29 }
--> { 2, 3, 7, 17, 19, 23, 29 }
--> { 2, 3, 11, 13, 17, 23, 31 }
--> { 2, 3, 11, 13, 19, 23, 29 }
--> { 2, 3, 13, 17, 19, 23, 23 }
--> { 2, 5, 7, 11, 13, 19, 43 }
--> { 2, 5, 7, 11, 13, 31, 31 }
--> { 2, 5, 7, 11, 17, 29, 29 }
--> { 2, 5, 7, 13, 17, 19, 37 }
--> { 2, 5, 7, 13, 19, 23, 31 }
--> { 2, 5, 11, 13, 17, 23, 29 }
--> { 2, 5, 11, 17, 19, 23, 23 }
--> { 2, 7, 11, 13, 17, 19, 31 }
--> { 2, 3, 5, 7, 11, 13, 17, 19, 23 }

If anyone wants the source, I can share it here