The smallest primep such that the sum of
k-th powers of all successive gaps between primes up
to p, for k = 1 through 7, are all primes.
Note further how this prime curiously is made up of smaller
primes in more than one way:
541-613-71-3 ;
541-613-7-13 ;
541-61-37-13 ;
541-61-3-71-3
;
541-61-3-7-13
;
5-41-613-71-3
;
5-41-613-7-13
; etc. [Beedassy]