The last 1000 numbers that are not the sum of fourth powers of distinct primes.

334973813847, 334973814472, 334974632247, 334974632872, 334982000727, 334982001352, 334983614007, 334983614632, 334984580727, 334984581352, 334987715367, 334987715992, 334990988967, 334990989592, 334991235447, 334991236072, 335001519447, 335001520072

1

The last such number is 340250525752, which is the fourth term of A121571. There are a total of 31332338304 numbers that cannot be written as the sum of fourth powers of distinct primes. See S001073 for the number of numbers between prime(i)^4 and prime(i+1)^4 that are not the sum of distinct fourth powers of primes.

T. D. Noe, Plot of 1000 terms

T. D. Noe, Table of 1000 terms

Wikipedia, Waring–Goldbach problem

Cf. A121571 (largest number that is not the sum of n-th powers of distinct primes), S001073.

nonn,hard,fini

T. D. Noe, Oct 02 2017