# Cunningham Number Factorizations

Numbers of the form b^n-1 and b^n+1 are factored for small prime bases b={2,3,5,7}

For b^n-1 and b^n+1, the first table of factorizations was published by Cunningham in 1925. Through various advancement in computing power and factorization methods, the tables have been extended. The most recently found entry for the tables here are for 3^619-1 (Feb 2017). The smallest numbers with unknown factorizations are as follows:

b -1 +1

2 1207 1033

3 661 589

5 431 373

7 359 331

## Examples

### Basic Examples

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In 1871, Aurifeuille discovered a factorization for 2^58+1:

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Wolfram Research, "Cunningham Number Factorizations" from the Wolfram Data Repository (2017) https://doi.org/10.24097/wolfram.67179.data