1. ## Number spirals

Consider the following:

81 82 83 84 85 86 87 88 89 90
80 49 50 51 52 53 54 55 56 91
79 48 25 26 27 28 29 30 57 92
78 47 24 09 10 11 12 31 58 93
77 46 23 08 01 02 13 32 59 94
76 45 22 07 00 03 14 33 60 95
75 44 21 06 05 04 15 34 61 96
74 43 20 19 18 17 16 35 62 97
73 42 41 40 39 38 37 36 63 98
72 71 70 69 68 67 66 65 64 99

It has several nice line patterns such as the squares of numbers, the oblong numbers, triangle numbers multiplied by 8 (e.g. 0, 8, 24, 48, 80 - incidentally when you add one to each of the foregoing numbers, you get the odd squares of numbers).

When you extend the spiral to 168, you get eight numbers in a row that are
prime (31, 13, 3, 5, 19, 41, 71, 109). The puzzle now is can you find a longer line of primes? How long?

For further exploration try triangle numbers or Fibonacci numbers (for historical notes I've partially explored this over 30 years ago).

2. ## Red faced

I didn't follow my own advice to do a Google search (my friend found the following website). Anyways you can check out this website:

NumberSpiral.com - Home

Enjoy.

3. ## One more note

Although I have heard of Ulam's spiral, I wasn't aware of its significance until just a few days ago which is very interesting.

4. Can the prime number string be lengthened by adjusting the number spiral? For example eliminating even numbers and numbers ending in 5?