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dollars amounts to approximately $13,500. The Fields Medal is considered the equivalent of the Nobel Prize in Mathematics (even though the money received is significantly less than the Nobel award).

Outside of the work he did to win the Fields Medal, perhaps Bombieri's most notable achievement is his improvement upon Linnik's "large sieve" method, which helped to demonstrate a result now known as "Bombieri's mean value theorem." Simply put, the theorem involves understanding the way prime numbers are distributed in arithmetic progressions.

Let's digress for a moment and recall that a prime number is a positive integer divisible only by itself and one. For example, 6 is not a prime because it has the divisors 1, 2, 3, and 6. But 11 is prime because its only divisors are 1 and 11. The sequence of primes begins 2, 3, 5, 7, 11, 13, 17, 19, ... and theorems concerning them are among the most beautiful in mathematics. Euclid proved in ancient times that there are infinitely many prime numbers and his proof still holds up as one of the clearest and most insightful to this day. Euclid proved we will never run out of primes but only continue to find more. For example, the currently largest known prime number is 2^30402457-1 found by Dr. Steven Boone and Dr. Curtis Cooper, both professors at Central Missouri State University. Their prime consists of 9,152,052 digits, yet many other people around the world at this moment are looking for a larger prime.

Perhaps my favorite sequence concerning prime numbers is the repunit primes. Repunits are simply copies of the digit 1 repeated: 1, 11, 111, 1111, 11111, ... and they have the formula, r(n) = (10^n1)/9. The only known values of n for which r(n) is prime are 2, 19, 23, 317, 1031, 49081, and 86453. To illustrate the intriguing and malleable nature of primes, we will create our own function involving r(n) to show how easy it is to find more of them. Letting z(n) = n * r(n) * 10^n + 1, (which has an unusual decimal expansion), z(n) is prime for n = 1, 5, 44, 56, 187, 192, 206, and there are no more up to n = 4,000.

But let's return to Bombieri.

He also spent some time working on the Riemann Hypothesis, which is currently regarded as the "Holy Grail" of mathematics. Anyone who solves it will immediately achieve immortality. Bombieri first read about the Riemann Hypothesis at the age of fifteen. Even though the problem is too advanced to fully explain here, suffice it to say that it concerns summing the infinite series: 1 + 1/2^s

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