OFFSET
0,1
COMMENTS
It is easy to see that there are no primes with more than one digit in the first 37 decimal places of (sqrt(3)-1)^(sqrt(2)-1). All primes with more than one digit end in 1, 3, 7, or 9. The only 1, 3, 7, or 9 in the first 37 decimal places of (sqrt(3)-1)^(sqrt(2)-1) is the 7 that is two digits after the decimal point. Since 87 = 3*29, there are no primes with more than one digit in the first 37 decimal places of (sqrt(3)-1)^(sqrt(2)-1). There are multidigit primes ending at the 38th decimal place, such as 41, 241, and 652241.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Bobby Jacobs, Prime Curios
EXAMPLE
0.8788022048554406482542450245650665224...
MAPLE
evalf((sqrt(3)-1)^(sqrt(2)-1), 110); # Muniru A Asiru, Oct 11 2018
MATHEMATICA
First@ RealDigits[N[(Sqrt[3] - 1)^(Sqrt[2] - 1), 120]] (* Michael De Vlieger, Sep 27 2016 *)
PROG
(PARI) (sqrt(3)-1)^(sqrt(2)-1) \\ Rick L. Shepherd, Nov 23 2016
(Magma) SetDefaultRealField(RealField(100)); (Sqrt(3)-1)^(Sqrt(2)-1); // G. C. Greubel, Oct 10 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Bobby Jacobs, Sep 27 2016
EXTENSIONS
Extended and offset corrected by Rick L. Shepherd, Nov 23 2016
STATUS
approved