## Prime number 131

$131$   is a prime number.

$130 \; = \; 2 \; \times \; 5 \; \times \; 13$
$132 \; = \; 2^2 \; \times \; 3 \; \times \; 11$

$131$   is the smallest prime for which each of the numbers   $p - 1$   and   $p + 1$
has at least three different prime divisors.

Find the next one

$139$   is a prime number.

$138 \; = \; 2 \; \times \; 3 \; \times \; 23$
$140 \; = \; 2^2 \; \times \; 5 \; \times \; 7$

curiously, each of the concatenations has at least three different prime divisors:

$(p-1) \; || \; (q-1)$
$(p+1) \; || \; (q+1)$

$130 || 138 \; = \; 130138 \; = \; 2 \; \times \; 31 \; \times \; 2099$
$132 || 140 \; = \; 132140 \; = \; 2^2 \; \times \; 5 \; \times \; 6607$

math grad - Interest: Number theory
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### 2 Responses to Prime number 131

1. paul says:

This is it

{139,{{2,1},{3,1},{23,1}},{{2,2},{5,1},{7,1}},140,138}

Paul.

• benvitalis says:

curiously, each of the concatenations has at least three different prime divisors:
130 || 138
132 || 140