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4383_Notes_3o2_fill

# 4383_Notes_3o2_fill - Math 4383 Section 3.2 Page 1 of 7...

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Math 4383 Section 3.2 Page 1 of 7 Number Theory Section 3.2 The Sieve of Eratosthenes How do you tell if a number is prime????? Great and INCREDIBLY nontrivial question! Obvious approach – Shorten the obvious approach – Then, how do we find all primes less than a particular number, n? Eratosthenes of Cyrene (276 – 194 BC) came up with a useful technique 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

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Math 4383 Section 3.2 Page 2 of 7 How many prime numbers are there? Answer – Euclid – infinitely many! Euclid’s Proof: Question – Is the product of the list of primes plus 1 actually a prime number?

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