Eratosthenes (276-194 BC) Historical Sketch
A very unusual man, Eratosthenes (pronounced "air-a-toss-the-nees"), ca. 276-194 BC, was born in Cyrene, a city in a part of ancient Egypt that is now in Libya. He was widely recognized by his contemporaries as a polymath, a person of wide learning,* and he was an intellectual descendent of Zeno of Elea, ca. 495-430 BC, in that he was devoted to high standards of logical rigor. His huge mental capacities were devoted to mathematics, astronomy, music, and poetry. Eratosthenes studied for a while in Athens, and in his middle thirties, he became the librarian at the famed library of Alexandria, Egypt (see http://cosmopolis.com), an esteemed position to say the least.
An outstanding piece of work by Eratosthenes was his measurement of the circumference of the Earth, a calculation of astonishing accuracy, as we now know. Another was his computation of the distances from the Earth to the Sun and to the Moon; and he also computed the tilt of the Earth's axis. In connection with astronomy, he also worked on a calendar and produced a catalog of stars.
Eratosthenes was also interested in pure mathematics. In fact, mathematicians all seem to like to tell about what is called the sieve of Eratosthenes, which is a marvelously simple method of listing the prime numbers. In this sieve, you first write down the positive integers beginning with 2 (since 1 is not a candidate for primality), which at the outset is
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 99 100 101
Then you cross out every multiple of the first number not crossed out. So the first step is to omit, not 2, but every multiple of 2. The next table shows, by means of their omission, which numbers are left after this first step.
2 3 5 7 9 11 13 15 17 19 21 23 25
27 29 31 33 35 37 39 41 43 45 47 49 51
53 55 57 59 61 63 65 67 69 71 73 75
77 79 81 83 85 87 89 91 93 95 97 99 101
The next number not crossed out is 3, so now omit every third number after 3 (lots have already been omitted, of course). The result is
2 3 5 7 11 13 17 19 23 25
29 31 35 37 41 43 47 49
53 55 59 61 65 67 71 73
77 79 83 85 89 91 95 97 101
The next number not already omitted is 5, so now omit every fifth number after 5, and the result is
2 3 5 7 11 13 17 19 23
29 31 37 41 43 47 49
53 59 61 67 71 73
77 79 83 89 91 97 101
The next number not already omitted is 7, so now omit every seventh number after 7, and the result is
2 3 5 7 11 13 17 19 23
29 31 37 41 43 47
53 59 61 67 71 73
79 83 89 97 101
At this stage, what is left is all the primes less than or equal to 101. You can be sure that they are prime since the square roots of all those listed are greater than 7. This particular sieve method, and its basic idea, has led to more recent "sieve methods" in other areas of mathematics.
It is generally agreed that Eratosthenes committed suicide by self-imposed starvation, and some historians believe he did such to fulfill a prediction he made as to the age he would be at death.
*T. L. Heath, A History of Greek Mathematics, Oxford, 1921.