Problems Set at an Oral Examination.
Assume that p and q are two successive prime numbers, Can their sum be a prime number?

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Solution

Yes,
It can be possible when $p = 2$ and $q = 3$ then $p + q = 5$ which is prime.

But this is the only example.
After this , any two prime numbers $p$ and $q$ will be odd and their sum $p + q$ will be even and hence will never be odd.

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Similar questions

a, b

State true (T) of false (F):

$(i)$ The sum of primes cannot be a prime.

$(i i)$ The product of primes cannot be a prime.

$(i i i)$ An even number is composite.

$(i v)$ Two consecutive numbers cannot be both primes.

$(v)$ Odd numbers cannot be composite.

$(v i)$ Odd numbers cannot be written as sum of primes.

$(v i i)$ A number and its successor are always co-primes.

43361

p_{1}, p_{2}

42900

43361

p_{1} + p_{2}

40,

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