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It will be quicker to try different powers of two, and seeing if the remainder is prime.

127 = 1 + 126, 126 isn't prime

127 = 2 + 125, 125 isn't prime

127 = 4 + 123, 123 isn't prime

127 = 8 + 119, 119 isn't prime

127 = 16 + 111, 111 isn't prime

127 = 32 + 95, 95 isn't prime

127 = 64 + 63, 63 isn't prime

127 < 128, so all the possibilities are exhausted.

So, 127 can't be expressed as a sum of a prime and a power of two.

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Q: Can 127 can be written in the form of sum of prime number and a power of 2?
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