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Power Difference Prime

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The name power difference prime is used here for a prime number of the form n^n-(n-1)^(n-1), where n is an integer with n>=2. The reported indices, including probable prime candidates, are n=2, 3, 4, 7, 11, 17, 106, 120, 1907, 7918, ... (OEIS A072164). Haga knew the first four indices and Rivera found the next five, with the value at n=1907 reported as only a probable prime (Rivera 2002). The value at n=7918 was reported by H. Lifchitz in 2001 (Andersen 2005).

See also

Integer Sequence Primes, Power Tower

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References

Update a linkAndersen, J. K. "RE: Is There a Pattern?" Nov. 28, 2005. http://groups.yahoo.com/group/primenumbers/message/17255Rivera, C. "Puzzle 185. Differences Between Consecutive n^n Values." 2002. https://www.primepuzzles.net/puzzles/puzz_185.htm.Sloane, N. J. A. Sequence A072164 in "The On-Line Encyclopedia of Integer Sequences."Update a linkUnderwood, M. "RE: Is There a Pattern?" Nov. 28, 2005. http://groups.yahoo.com/group/primenumbers/message/17254

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Power Difference Prime

Cite this as:

Weisstein, Eric W. "Power Difference Prime." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PowerDifferencePrime.html

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