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MATHEMATICA
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NextPrime[ n_Integer ] := Module[ {k}, k = n + 1; While[ ! PrimeQ[ k ], k++ ]; k ]; c = d = p = q = 0; Do[ While[ d++; d <= 10^n, q = NextPrime[ q ]; p = p + Apply[ Plus, RealDigits[ q ] [[ 1 ] ]]; If[ PrimeQ[ p ], c++ ]]; d--; Print[ c ], {n, 0, 10} ]
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