Prime Curios!: 2063

2063
(another Prime Pages' Curiosity)

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The concatenation of 2063 with the 2063rd prime is prime:

(17987) = 2063, and 206317987 is prime.

2063 is the smallest prime that is the start of 6 consecutive primes containing all even digits except for the last digit: 2063, 2069, 2081, 2083, 2087, 2089; 2063 is the smallest prime that is the sum of the 53 consecutive composite numbers: 2063 = 1+4+6+8+9+...+72+74: note that 53 is also prime.

The sum of the digits of the 2063rd Fibonacci number, when expressed in the prime bases 2, 3, 5, and 7, are primes.

A cube with a prime volume of 2063 has faces where the integer part of their area is also prime: 93701.

2063 is the smallest prime that is the start of 6 (and only 6) consecutive primes whose digit sums are prime: the digit sums of 2063, 2069, 2081, 2083, 2087, 2089 are prime, however 2099's digit sum is composite; given f(x) = (x-1)*5^(x-1)/5, 2063 is the largest known prime p such that the sum f(1)+f(2)+...+f(p) is prime: the sum is a 1015 digit prime: 9734753361...0980834961. [Noll]

Submitted: 2009-07-05 04:40:46; Last Modified: 2009-10-09 20:39:38.