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

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

Offset

4,1

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.

Links

Table of n, a(n) for n=4..12.

Wikipedia, Circular prime.

Example

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.

Crossrefs

Cf. A016114, A293663, A293660, A327811.

Sequence in context: A274816 A216902 A327811 * A295468 A257913 A346495

Adjacent sequences: A327832 A327833 A327834 * A327836 A327837 A327838

Keyword

nonn,base,more

Author

Giovanni Resta, Sep 27 2019

Status

approved