Template:Sequence of the Day for August 10

Intended for: August 10, 2011

Timetable

• First draft entered by Alonso del Arte on May 8, 2011 ✓
• Draft reviewed by Daniel Forgues on August 7, 2011 ✓
• Draft approved by Mitch Harris August 9, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

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A069567: Smaller of two consecutive primes which are anagrams of each other (base 10).

{ 1913, 18379, 19013, 25013, 34613, 35617, 35879, ... }

The 293^rd prime is 1913. The 294^th prime is 1931. It just so happens that both of these are anagrams of their base 10 digits, namely: two 1s, a 3 and a 9. These pairs of primes are called Ormiston pairs or rearrangement prime pairs. (An Ormiston pair can be generalized to an Ormiston k-tuple:

k

consecutive primes which are anagrams.) The relation of the prime counting function is important; it is not enough for the two primes to be anagrams, it must also be the case that

π (Op1 ) = π (Op2 )  −  1

. Thus, 179 and 197 don’t count as an Ormiston pair because

π (179) = 41

and

π (197) = 45

.

See:

* Jens Kruse Andersen, Ormiston Tuples, 2007.