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Two Theorems on Mosaics

  • B. Gordon (a1) and M. M. Robertson

Extract

The concept of a mosaic was recently introduced by A. A. Mullin (1). By the fundamental theorem of arithmetic, every integer n > 1 can be uniquely expressed in the form

where the pi are primes satisfying p1 < p 2 < . . . < pr . We then express any exponents aj which are greater than unity in the same manner, and continue in this way until the process terminates. The resulting planar configuration of primes is called the mosaic of n.

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References

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1. Mullin, A. A., Some related number-theoretic functions, Bull. Amer. Math. Soc., 69 (1963), 446447.
2. Rosser, J. B., The rith prime is greater than n log n, Proc. London Math. Soc, 45 (1939), 2144.
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