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Decimal expansion of (sqrt(3)-1)^(sqrt(2)-1).
1

%I #31 Sep 08 2022 08:46:17

%S 8,7,8,8,0,2,2,0,4,8,5,5,4,4,0,6,4,8,2,5,4,2,4,5,0,2,4,5,6,5,0,6,6,5,

%T 2,2,4,1,5,8,9,5,1,5,9,1,8,6,3,1,8,0,6,4,9,3,1,3,7,3,4,1,5,2,8,8,8,0,

%U 5,3,8,3,0,0,7,8,7,2,3,8,7,6,3,4,7,7,0,4,0,7,3,7,6,0,7,3,0,9,6,8,2,1,4,4,7

%N Decimal expansion of (sqrt(3)-1)^(sqrt(2)-1).

%C 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.

%H G. C. Greubel, <a href="/A277064/b277064.txt">Table of n, a(n) for n = 0..10000</a>

%H Bobby Jacobs, <a href="https://primes.utm.edu/curios/page.php?number_id=11586">Prime Curios</a>

%e 0.8788022048554406482542450245650665224...

%p evalf((sqrt(3)-1)^(sqrt(2)-1),110); # _Muniru A Asiru_, Oct 11 2018

%t First@ RealDigits[N[(Sqrt[3] - 1)^(Sqrt[2] - 1), 120]] (* _Michael De Vlieger_, Sep 27 2016 *)

%o (PARI) (sqrt(3)-1)^(sqrt(2)-1) \\ _Rick L. Shepherd_, Nov 23 2016

%o (Magma) SetDefaultRealField(RealField(100)); (Sqrt(3)-1)^(Sqrt(2)-1); // _G. C. Greubel_, Oct 10 2018

%K nonn,cons

%O 0,1

%A _Bobby Jacobs_, Sep 27 2016

%E Extended and offset corrected by _Rick L. Shepherd_, Nov 23 2016