Consider the following statements:
- For every positive integer $n,$ let $\#{n}$ be the product of all primes less than or equal to $n.$
Then, $\# {p}+1$ is a prime, for every prime $p.$
- $\large\pi$ is a universal constant with value $\dfrac{22}{7}.$
- No polynomial time algorithm exists that can find the greatest common divisor of two integers given as input in binary.
- Let $L \equiv \{x \in \{0,1\}^{*}\mid x \text{ is the binary encoding of an integer that is divisible by 31}\}$
Then, $L$ is a regular language.
Then which of the following is TRUE ?
- Only statement (i) is correct.
- Only statement (ii) is correct.
- Only statement (iii) is correct.
- Only statement (iv) is correct.
- None of the statements are correct.