Mathematicians love prime numbers in much the same way that chemists love atoms and biologists love genes. Just as atoms are the building blocks of the matter around us and genes are the building blocks of life, prime numbers are the building blocks of mathematics.
Hence, the study of prime numbers has had a tremendous impact on everything from illuminating unexplored areas of pure mathematics to inspiring new technologies for protecting our most secret communications.
Prime numbers, for those who have forgotten, are those numbers that cannot be divided by any other number except 1 and itself. So 5 is prime because nothing will divide into it, but 6 is not prime because it can be divided by 2 and 3. All numbers can be broken down into a series of one or more primes multiplied together, so the prime 5 is just 5, while 6 is 2
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centered figurate numbers
I made a program that compiles centered figurate numbers. The sum of the centered numbers - or pronic numbers if that is the right term - contain no primes using numbers 8 and 9. I have checked numbers up to 100, and primes up to 100,000, and it seems strange that only these two sequences are free of primes. The fact that figurate numbers 1 to 7 produce primes seemed at first insignificant, given that shapes can only be made using 3 or more numbers, unless supposing a shape using two would be a line, and one being an expanding point! Then it looks like the first seven numbers are significant, with 8 and 9 being an end, or beginning of another 'sequence'. All the numbers in the 9 sequence have digits that sum to 10, and all 8 pronics are squares, which explains why they can't be primes, but squares of odd numbers in the sequence of odd numbers. All very odd, and I have now just learned from the program The Story of Maths, that a square of 8 units on a side is close to the volume of a circle of diameter 9. 8 and 9 do seem to be significant, but how?
I was also struck by the fact that there are 7 crystal systems: from Cubic to Triclinic.
Is this just a arithmetical anomaly or does it have any meaning.