Question

This article says:

Every prime number can be expressed as
30k±1, 30k±7, 30k±11, or
30k±13 for some k.
That means we can use eight bits per
thirty numbers to store all the
primes; a million primes can be
compressed to 33,334 bytes

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“That means we can use eight bits per thirty numbers to store all the primes”

This “eight bits per thirty numbers” would be for k, correct? But each k value will not necessarily take-up just one bit. Shouldn’t it be eight k values instead?

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“a million primes can be compressed to 33,334 bytes”

I am not sure how this is true.

We need to indicate two things:

• VALUE of k (can be arbitrarily large)

• STATE from one of the eight states (-13,-11,-7,-1,1,7,11,13)

I am not following how “33,334 bytes” was arrived at, but I can say one thing: as the prime numbers become larger and larger in value, we will need more space to store the value of k.

How, then can we fix it at “33,334 bytes”?

Answer 1

You don’t need to store each value of k. If you want to store the prime numbers below 1 million, use 33,334 bytes – the first byte corresponds to k=0, the second to k=1 etc. Then, in each byte, use 1 bit to indicate “prime” or “composite” for 30k+1, 30k+7 etc.