Pensieve header: Solution to Itai’s 180905 riddle.

Total[Last/@FactorInteger [#]]&/@ (6 1001+{7,11,13,7 11,7 13, 11 13})

FactorInteger[6 1001+7]

Total[Last/@FactorInteger [#]]&/@ (12 1001+{7,11,13,7 11,7 13, 11 13})

PrimeQ@Echo[7 11+11 13+13 7]