The smooth integers [Les entiers friables].

The so-called smooth integers are the integer numbers with very small prime factors (2, 3, 5,...) and then easy to factorize.

The bottom line defines the arbitrary colors used (randomly chosen in order that two consecutive prime numbers do not look like ...) for the 31 useful prime numbers {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127} from left to right.

Each vertical grey line displays an integer number N inside [2,130]: the little spheres are its prime factors Pi, with their radius being an increasing function -the square root- of the exponent of Pi.

The horizontal grey lines display the 31 prime numbers.

See some related pictures (including this one):





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