Any whole number that’s not a prime is the sumof two primes
but this is wholly false; for instance, the number 123 is not a prime (it’s 3x41) and is not the sum of two primes (it can’t be the sum of two odd primes since it’s odd itself; the only even prime is 2, and the thing it’s the-sum-of-2-and is 121, which is a square and therefore not a prime).
There’s a famous conjecture (not proven as yet, though there was some exciting progress a couple of years back) saying that any even number from 4 up is the sum of two primes, but that’s not the same thing.
The philosophical quibble: Then you say, after talking a bit more about making integers by adding up primes,
That’s why primes are a little like the chemical elements
which seems quite wrong to me; there is an analogy between the chemical elements and the prime numbers, but it’s about multiplication (every positive integer is the product of primes in essentially one way), not about addition (typically numbers are the sums of primes in many many ways).
A correction and a philosophical quibble.
The correction: You say
but this is wholly false; for instance, the number 123 is not a prime (it’s 3x41) and is not the sum of two primes (it can’t be the sum of two odd primes since it’s odd itself; the only even prime is 2, and the thing it’s the-sum-of-2-and is 121, which is a square and therefore not a prime).
There’s a famous conjecture (not proven as yet, though there was some exciting progress a couple of years back) saying that any even number from 4 up is the sum of two primes, but that’s not the same thing.
The philosophical quibble: Then you say, after talking a bit more about making integers by adding up primes,
which seems quite wrong to me; there is an analogy between the chemical elements and the prime numbers, but it’s about multiplication (every positive integer is the product of primes in essentially one way), not about addition (typically numbers are the sums of primes in many many ways).
Thanks for the catch! I’ll put in a correction and credit you at the bottom.