Well there are other possiblities too..but im just considering the first set n obviously the easier one to figure out... :P
The first (and smallest) set that I could think of immediately was 97+3. But, your answer is acceptable too. So, congrats
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.
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
Thanx everyone !! :happy: :happy: :happy: :happy: But, my code had a little bug which gave a few (15%) invalid outputs like : The bug is fixed now. (2day morning) And, I will soon post this as an article as shabbir said. And BTW, the correct list is here : (198 different unique sets, not 233) Code: (~) Found 6 ways of expressing 100 as a sum of 2 primes. --> { 3, 97 } --> { 11, 89 } --> { 17, 83 } --> { 29, 71 } --> { 41, 59 } --> { 47, 53 } (~) Found 3 ways of expressing 100 as a sum of 3 primes. --> { 2, 19, 79 } --> { 2, 31, 67 } --> { 2, 37, 61 } (~) Found 64 ways of expressing 100 as a sum of 4 primes. --> { 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, 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, 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, 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, 13, 19, 61 } --> { 7, 13, 37, 43 } --> { 7, 17, 23, 53 } --> { 7, 17, 29, 47 } --> { 7, 19, 31, 43 } --> { 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 } (~) Found 55 ways of expressing 100 as a sum of 5 primes. --> { 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, 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, 11, 23, 59 } --> { 2, 5, 11, 29, 53 } --> { 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, 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, 19, 29, 43 } --> { 2, 7, 19, 31, 41 } --> { 2, 7, 23, 31, 37 } --> { 2, 11, 13, 31, 43 } --> { 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 } (~) Found 34 ways of expressing 100 as a sum of 6 primes. --> { 3, 5, 7, 11, 13, 61 } --> { 3, 5, 7, 11, 31, 43 } --> { 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, 11, 13, 31, 37 } --> { 3, 5, 11, 17, 23, 41 } --> { 3, 5, 13, 17, 19, 43 } --> { 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, 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, 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, 17, 19, 23, 29 } --> { 5, 11, 13, 17, 23, 31 } --> { 5, 11, 13, 19, 23, 29 } --> { 7, 11, 13, 17, 23, 29 } (~) Found 35 ways of expressing 100 as a sum of 7 primes. --> { 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, 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, 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, 17, 19, 23, 29 } --> { 2, 3, 11, 13, 17, 23, 31 } --> { 2, 3, 11, 13, 19, 23, 29 } --> { 2, 5, 7, 11, 13, 19, 43 } --> { 2, 5, 7, 13, 17, 19, 37 } --> { 2, 5, 7, 13, 19, 23, 31 } --> { 2, 5, 11, 13, 17, 23, 29 } --> { 2, 7, 11, 13, 17, 19, 31 } (~) Found 1 ways of expressing 100 as a sum of 9 primes. --> { 2, 3, 5, 7, 11, 13, 17, 19, 23 } @shabbir: Can we have a separate section for submitting source-codes instead of posting them in the articles section ? Of course there is no problem with posting them as article, 'coz some explanation is included with the source code; but I think the tutorial articles and source codes get mixed this way.
great saswat, i have seen your work, it's really good and awesome, also the question you asked is great if we can have source-code section.