Redmond–Sun conjecture

In mathematics, the Redmond–Sun conjecture, raised by Stephen Redmond and Zhi-Wei Sun in 2006, states that every interval [x^m, yⁿ] with x, y, m, n ∈ {2, 3, 4, ...} contains primes with only finitely many exceptions. Namely, those exceptional intervals [x^m, yⁿ] are as follows:

[2^{3},\,3^{2}],\ [5^{2},\,3^{3}],\ [2^{5},\,6^{2}],\ [11^{2},\,5^{3}],\ [3^{7},\,13^{3}],

[5^{5},\,56^{2}],\ [181^{2},\,2^{15}],\ [43^{3},\,282^{2}],\ [46^{3},\,312^{2}],\ [22434^{2},\,55^{5}].

The conjecture has been verified for intervals [x^m, yⁿ] below 10¹². It includes Catalan's conjecture and Legendre's conjecture as special cases. Also, it is related to the abc conjecture as suggested by Carl Pomerance.

External links

Redmond-Sun conjecture at PlanetMath.org.
Number Theory List (NMBRTHRY Archives) --March 2006
Sequence A116086 in the On-Line Encyclopedia of Integer Sequences

Prime number conjectures

Hardy–Littlewood 1st 2nd Agoh–Giuga Andrica's Artin's Bateman–Horn Brocard's Bunyakovsky Chinese hypothesis Cramér's Dickson's Elliott–Halberstam Firoozbakht's Gilbreath's Grimm's Landau's problems Goldbach's weak Legendre's Twin prime Legendre's constant Lemoine's Mersenne Oppermann's Polignac's Pólya Redmond–Sun Schinzel's hypothesis H Waring's prime number

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