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The same applies to any set of the first n primes. Each prime generates a waveform that destructively adds. 2 eliminates all even numbers. 3 eliminates all mult
by goldenkey 9y ago
The same applies to any set of the first n primes. Each prime generates a waveform that destructively adds. 2 eliminates all even numbers. 3 eliminates all multiples of 3 - but has some overlap with 2.
Turns out the additive sequence to never hit any multiples of 2 or 3 is {+4, +2}
Not much more complex than 'only the odd squares' yet now we are eliminating many more false positives.
We can continue to construct the additive sequences for the first N primes. This is known as the First Differences of Reduced Residue Systems Modulo Primorials. Hardy and Littlewood studied the statistical dynamics of these ordered sets.