Prime number conjectures

A question is this type if and only if it involves proving or disproving statements about prime numbers, such as '2ⁿ - 1 is prime' or 'sum of consecutive primes is a multiple of 5'.

3 questions · Standard +0.4

1.01a Proof: structure of mathematical proof and logical steps

Sort by: Default | Easiest first | Hardest first

OCR MEI C3 2008 January Q5

4 marks Moderate -0.8

Verify the following statement: $$\text { ' } 2 ^ { p } - 1 \text { is a prime number for all prime numbers } p \text { less than } 11 \text { '. }$$
Calculate $23 \times 89$, and hence disprove this statement: $$\text { ' } 2 ^ { p } - 1 \text { is a prime number for all prime numbers } p ^ { \prime } \text {. }$$

OCR H240/02 2019 June Q6

4 marks Standard +0.8

6 Shona makes the following claim.
" $n$ is an even positive integer greater than $2 \Rightarrow 2 ^ { n } - 1$ is not prime"
Prove that Shona's claim is true.

SPS SPS SM Pure 2021 May Q6

4 marks Challenging +1.2

Shona makes the following claim. "$n$ is an even positive integer greater than $2 \Rightarrow 2^n - 1$ is not prime" Prove that Shona's claim is true. [4]