Study of Totatives and Prime Argam

The argam numeral set is defined by the prime decomposition of the integer symbolized. Multiplicative exercises like writing an “infinite multiplication table” as on the previous page serve to help generate composite argam. Since the primes are not efficiently studied this way, I used the sexagesimal totatives to locate primes. The top left chart isolates primes less than 120 using a modulus of 6. With (mod 6), primes greater than the prime divisors of 6 will occupy ±1 (mod 6). The chart to the right of this, “Sexagesimal Totatives”, identifies the integers 0 ≤ n ≤ 60 that are coprime to 60. These 16 totatives are further classified according to their residue (mod 4) and (mod 6) at far right. The full-width chart “Primes Pre 79ab” identifies the primes less than 540 (sexagesimal 90) using the sexagesimal totatives (mod 60), a sieve which is slightly more efficient but also more complex than (mod 6). The argam for primes greater than 83 are stylized vertically stacked abbreviations for the chemical elements. These charts were written 12 July 2007, tayya 79b1. The chart at the bottom, “Prime Number Names Taken from the Chemical Elements”, simply assigns a chemical element whose atomic number (x = PrimePi[x]) to a prime with a corresponding π(x). This chart’s range is slightly greater than the above chart. This chart developed 17 July 2007, tayya 79b6, (Salcyra Karlmelal, “Life Phase of Karl Michael, Son”), St. Louis. This page likely developed after a study first penned at s7836a53.

This page last modified Friday 13 April 2012.