Sum of prime numbers 2 to 23 = 100, a perfect square
The next such sum is beyond the prime numbers under 20,000
Sum of prime numbers 2 to 22073 =25633969 Sq. root =5063
The next one goes beyond prime numbers under 60,000
Sum of prime numbers 2 to 67187 =212372329 Sq. root =14573
Next one is further beyond.
Sum of prime numbers 2 to 79427 =292341604 Sq. root=17098
Conjecture 28. Is 2+3+5+7+… n /= x^y when y >2 ,where n is the nth prime number. This has been confirmed for all primes upto 10^5 and upto y=10. Conjecture 29. Is x^y – 2+3+5+7+… n =1 for y>1 where n is the nth prime number other than the case (21^2)-2+3+5+7+… 59=1. In the case of n=2 there is finitely many solutions. So for any higher power greater than two is there no solutions i.e the only consecutive powers are the square powers. This has been confirmed upto 10^5.For all primes upto 10^5 there is only four such solutions for the case n=2.
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Conjecture no.30 Is there infinitely many prime sums that sum to a prime infinitely often i.e that 2+3+5+7+…n= a prime infinitely often. Many of these conjectures were inspired by Fermat’s Last Theorem and Catalan’s Conjecture. Thank you, Nunghead
My Mathematics work and other extraneous diversions 
Conjectures 27 and 28 have been also conjectured by G.L Honaker Jr, editor of Prime Curios and also is a contributor to The Prime Puzzles maintained by Carlos Rivera.
A small case of the conjecture i.e the fact that the sum of the first nine primes sum to 100 was observed independently by G.L Honaker Jr, Contributor Moddy of the Prime Curios site and Nunghead at numeracy.car.blog.
See the links below on the evolution of this conjecture.
https://primes.utm.edu/curios/page.php/100.html -See first line
https://primepuzzles.net/puzzles/puzz_009.htm
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