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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

(5704 elements)

Retrieve the resource:

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Retrieve the default content:

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

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Various entries are not completely factored:

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Many of the factorizations have odd patterns within the digits, such as 2^995+1:

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The factorization of 3^336+1 has odd patterns in ternary:

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