# If an integer greater that 4 is a perfect square, then the immediately preceding integer is not prime.

allhvasstH 2020-11-10 Answered
If an integer greater that 4 is a perfect square, then the immediately preceding integer is not prime.
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## Expert Answer

berggansS
Answered 2020-11-11 Author has 91 answers
Proof:
Consider integer greater than 4, which is a perfect square.

Now we will show that the immediately preceding integer is not a prime.
Hence,

$⋮$

Therefore, we can see that all numbers have two factors which are greater than one.
Further, we know that the prime number is a number that is divisible only by itself and 1. Thus, numbers that have more than two factors are not primes.
Now, we can conclude that, if an integer greater than 4 is a perfect square, then the immediatelly preceding integer is not prime.
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