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  There Is NoLargest PrimeNumberEuklidResults Proof of the MainTheorem There Is No Largest Prime Number With an introduction to a new proof techniqueEuklid of Alexandria Department of MathematicsUniversity of Alexandria 27th International Symposium on Prime Numbers, –280ResultsProof of the Main Theorem  There Is NoLargest PrimeNumberEuklidResults Proof of the MainTheorem There Is No Largest Prime Number The proof uses  reductio ad absurdum  . Theorem There is no largest prime number. Proof. 1. Suppose  p   were the largest prime number.2. Let  q   be the product of the first  p   numbers.3. Then  q   +1 is not divisible by any of them.4. Thus  q   +1 is also prime and greater than  p  .
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