20070801, 04:01  #1 
2^{4}·5·59 Posts 
Numbered Triangle: (lack of)Prime Patterns
My first post here, Hi All.
Assume we arrange numbers like this. Code:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 1 3never 0 prime rows in between 2 5never 1 prime rows in between 4 8primes 7 12never 2 prime rows in between 11 17primes 16 23primes 22 30never 3 prime rows in between 29 38primes 37 47primes 46 57primes 56 68never 4 prime rows in between 67 80primes 79 93primes 92 107primes 106 122primes 121 138never 5 prime rows in between The gap between a diagonal column never containing a prime starts at 0 and increases by one. I've tested this for a few thousand rows and it holds true. My question is why? What is happening here? Obviously I assume this has to do with ordering the numbers in such a fashion. But for the life of me I cannot understand why this is happening. Any nudge in the right direction would be appreciated. Thanks 
20070801, 14:52  #2 
"William"
May 2003
New Haven
23·103 Posts 

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