Prime Problems.txt

A048597 "Very round numbers: reduced residue system consists of only primes and 1."
    - finite (10)
    - 1, 2, 3, 4, 6, 8, 12, 18, 24, 30

A000040 "The prime numbers."
    - infinite
    - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
    
30:
    - becomes 8 when passed through Euler's Totient Function
    
89:
    - the smallest circular number (89 = 9+8+7+6+5+4+3+2+1+2+3+4+5+6+7+8+9)
    - the 24th prime number
    - the first 89 digits of pi sum to 432
    
Notes:
    A048597 is finite and has 10 entries, A048597's last entry is 30, and there are 10 primes below 30.

Bitwise Tricks:

var w = -1L; // all bits
var x = (w & (-6148914691236517206L /* ‭10101010101010101010101010101010 | 10101010101010101010101010101010‬; mask out factors of two*/));
var y = (x & 7905747460161236406L   /* ‭‭01101101101101101101101101101101 | 10110110110110110110110110110110‬‬; mask out factors of three*/);
var z = (y & (-1190112520884487202L /* ‭11101111011110111101111011110111 | 10111101111011110111101111011110‬‬‬‬; mask out factors of five*/));

Products:
    2 x 3 x 5 = 30.
    All values A048597 = 179159040.
    The first 10 values in A000040 = 6469693230.
    The first 8 values in A000040 = 9699690.