Number Theory


On Prime Factors in Old and New Sequences of Integers

Authors: Marco Ripà

The paper shows that the only possible prime terms of the "consecutive sequence" (1,12,123,1234...) represent of the total, and their structure is explicited. This outcome is then extended to every permutation of their figures. The previous result is applied to a consistent subset of elements belonging to the circular sequence (resulting from the consecutive one), identifying moreover the 31 first primes. Therefore, a criterion is illustrated (further extendible) that progressively reduces the numerousness of the "candidate prime numbers". Section 3.3 is devoted to the solution of a similar problem. The last section introduces a new sequence which, although much larger, has the same properties as the previous ones, and it also proposes a few open problems.

Comments: This paper is 17 pages long and the Italian version has already been published here: (

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Submission history

[v1] 28 Jan 2011
[v2] 4 Mar 2011

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