2017•viXraOpen access

Large primes obtained concatenating the numbers P-d(k) where d(k) are the prime factors of the Poulet number P

Marius Coman

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Abstract

In this paper I conjecture that there are an infinity of primes which can be obtained concatenating the numbers P - d(1); P - d(2); ...; P – d(k); P, where d(1), ..., d(k) are the prime factors of the Poulet number P. Example: using the sign “//” with the meaning “concatenated to”, for the Poulet number 129921 (= 3*11*31*127), the number (129921 – 3)//(129921 – 11)//(129921 – 31)//(129921 – 127)//129921 = 129918129910129890129794129921 is prime. Note that such primes are obtained for 10 from the first 90 Poulet numbers!

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What this paper is about

In this paper I conjecture that there are an infinity of primes which can be obtained concatenating the numbers P - d(1); P - d(2); ...; P – d(k); P, where d(1), ..., d(k) are the prime factors of the Poulet number P. Example: using the sign “//” with the meaning “concatenated to”, for the Poulet number 129921 (= 3*11*31*127), the number (129921 – 3)//(129921 – 11)//(129921 – 31)//(129921 – 127)//129921 = 129918129910129890129794129921 is prime. Note that such primes are obtained for 10 from the first 90 Poulet numbers!

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Available abstract

In this paper I conjecture that there are an infinity of primes which can be obtained concatenating the numbers P - d(1); P - d(2); ...; P – d(k); P, where d(1), ..., d(k) are the prime factors of the Poulet number P. Example: using the sign “//” with the meaning “concatenated to”, for the Poulet number 129921 (= 3*11*31*127), the number (129921 – 3)//(129921 – 11)//(129921 – 31)//(129921 – 127)//129921 = 129918129910129890129794129921 is prime. Note that such primes are obtained for 10 from the first 90 Poulet numbers!

Key concepts: Mathematics, Number theory, Combinatorics, Conjecture, Infinity, Sign (mathematics), Prime (order theory), Prime number

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