1960 AHSME Problems/Problem 33
Problem
You are given a sequence of terms; each term has the form where stands for the product of all prime numbers less than or equal to , and takes, successively, the values . Let be the number of primes appearing in this sequence. Then is:
Solution
First, note that does not have a prime number larger than as one of its factors. Also, note that does not equal .
Therefore, since the prime factorization of only has primes from to , and share at least one common factor other than . Therefore is not prime for any , so the answer is .
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 32 |
Followed by Problem 34 | |
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