>>11847201Consider the following: our number base, 10, has the factorization 2 x 5. Let us apply a partial, ad-hoc sieve of Eratosthenes to the range 1-100, taking only these factors into account, viz:
1) Blot out the unit, which is neither prime nor composite,
2) Blot out all evens (multiples of two), save two itself, and
5) Blot out all (remaining) multiples of five, save five itself.
What remains is a set of 41 numbers, consisting of the 25 primes less than 100 (a convenient fact, exactly 25% of the range is in fact prime), plus another 16 composite numbers. It is these 16 composites which are of some interest, as they contain a few "pseudo-primes" which seem at a glance like they might be prime. This small group of numbers includes Grothendieck's prime, 57.
Everything north of our base, 10, is a candidate at this point (because the ending digits 1,3,7 and 9 are precisely those less than 10 yet co-prime to 10. Although subjective, the graphic shows a series of "obvious" multiples and squres which are learned in early childhood. This leaves about 3-5 "pseudo-primes", of which Grothendieck's is one. But the true subtlest of the bunch is 91, or 7 x 13. People don't see that shit coming.
Cognitively, I suspect that the additive process is far easier, (once our arbitrary base of 10 is learned and its rote arithmetic is taken for granted) while the subtractive one is that overlooked. Most everyone can reason very quickly that 63 must be a multiple of 3 just by looking at it, but not necessarily 57. Similar "logic" may apply to 87 and 51. Where the range 1-100 is concerned, simply asking "is it a multiple of three?" is enough to settle most "interesting" cases. The true special case is 91.
>>11847371>>11847814Doing a rote process in school yields several "useful" atomic facts, which are reinforced in basic job skills/counting during adult life. 51, 57 and 91 simply do not crop up very often in practical applications. Hence etc, get off your high horse.
