2. Let p; denote the ith prime integer (so that p = 2, p2 = 3,...

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2. Let p; denote the ith prime integer (so that p₁ = 2, p2 = 3, p3 = 5, and so on). Prove or disprove: For all n ≤ Z†, P1P2P3 · · · Pn + 1 is prime. 3. Prove that there are infinitely many prime integers. (Hint: Suppose there are only a finite number of primes, say P₁, P2, ..., Pn. Show that pip2 Pn+1 can be neither prime nor a product of primes.) 2. Let p; denote the ith prime integer (so that p₁ = 2, p2 = 3, p3 = 5, and so on). Prove or disprove: For all n ≤ Z†, P1P2P3 · · · Pn + 1 is prime. 3. Prove that there are infinitely many prime integers. (Hint: Suppose there are only a finite number of primes, say P₁, P2, ..., Pn. Show that pip2 Pn+1 can be neither prime nor a product of primes.)

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Answer 1The statement is true This can be proven by induction on n Base Case n 1 For n 1 P1P2P3P1 1 ... View the full answer