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We consider the numbers whose continued fraction expansions contain at least two partial quotients that are simultaneously large and prime, that is \\[ E'(\\phi):=\\Big\\{x\\in[0,1): \\exists\\, 1\\leq k\\neq l\\leq n, \\ a'_{k}(x),\\ a'_{l}(x)\\geq\\phi(n) \\ \\text{for i.m. } n\\in\\mathbb{N}\\Big\\}, \\] where $a'_i(x)$ denotes $a_i(x)$ if $a_i(x)$ is prime and $0$ otherwise. 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