A327835 Smallest circular prime with 12 digits in base prime(n).

2732225029, 314014500337, 1949332597181, 36440244156523, 123167650691711, 996133536974297, 12637043369352469, 26255687399203543, 182859787113571787

Offset: 4

Author

Giovanni Resta, Sep 27 2019

Keywords

• nonn
• base
• more

Comments

Excluding repunits, no circular primes with more than 12 digits are known, apart 58589854785907 that in base 11 has 14 digits. Also unknown are circular primes of length at least 12 in composite bases.

Repunits of 12 digits in any base b are not prime because they are always divisible by b+1.

a(4) = 2732225029 found by Felix Fröhlich.

Examples

			a(5) = 314014500337 = (111199AA988A)_11 is the smallest circular prime in base prime(5)=11 with 12 digits. By rotating its base 11 digits we obtain other 11 primes: 2881663478867, 2544462772057, 2513808162347, 2796333050257, 3107328801587, 3135601142617, 2852859684827, 2827155915937, 542325844787, 334614020137, and 315731126987.
		

Links

• Wikipedia, Circular prime.

Crossrefs

Cf. A016114, A293663, A293660, A327811.