Primes and factorials

Number Theory Level 1

Is there a prime number \(p\) that satisfies this inequality?

\[2018!+2 \le p \le 2018!+2018\]

Note: \(2018!\) is the factorial of 2018. That is, \(2018!=1 \times 2 \times 3 \times \cdots \times 2016 \times 2017 \times 2018.\)

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