Prime Distribution 2 and 5
I just considered that an interesting way to look at prime numbers is to look at what percentage of prime numbers end with each digit:
0: 0%
1: *unknown
2: infinitesimal% (specifically 1/(infinite value acheived)
3: *unknown
4: 0%
5: infinitesimal% (specifically 1/(infinite value acheived)
6: 0%
7: 0%
8: 0%
9: 0%
Now primes are also "sifted" from the pool of all numbers by identifying all numbers that can call known primes a factor, in increasing order. For this reason, while 2 has the lowest possible positive prime numbers associated with it (1, at 2), it has the highest percentage of numbers confirmed not to be prime out of any number, at precisely 50%-1 (itself). Since the digit 3 likely represents ~.25% of all primes and clears 1/6 of all primes minus 1 (itself)- it clears out every odd number with a factor of 3, which occurs every 6 digits, whereas every even number with a factor of 3 has already been sifted out by the process of the digit 2- this means two is definitely involved in (being the last digit or sifting out) more numbers from this perspective than three or any other digit.
1 and 9 are not prime in single digits, so 3 and 7 start with a lead initially and keep that lead through primes 1 to 100. Do prime distributions act geometrically? Can their momentum as a percentage of the whole per digit be tracked as an asymptote approaching 25% of the total, from either above or below that mark originally? If not asymptotic in this way, can the progression be tracked as a wave, oscillating each number above or below the 25% mark as they proceed? If these are not true then one or more of 1, 3, 7, 9 would need to become a clear leader at some point, pulling away from the crowd, and in an infinite pool of numbers dwarfing the remaining numbers to effectively infinitesimal percentages, even though the actual volume of numbers ending in those digits would be far greater than the actual volume of numbers ending in 2 or 5. This is because unless functional infinity is considered, any finite number over an infinite value ends up being infinitesimal as a percentage.
Comments
Post a Comment