so then euclid goes one step further. and that's the point. having identified the primes, we can now ask questions like, how many of them are there? and what euclid proved is that there are an infinite number. so let's see how he did it. euclid's proof of the infinitude of primes shows that if we multiply together any finite collection of primes and then add 1, the resulting sum is not divisible by any of the primes that we start with. for example, multiply the prime numbers 2, 3, and 5 and then add 1. the result is 31, a number which can't be divided by either 2, 3, or 5. but in fact, 31 is itself prime, so we've discovered a new prime number! now, if we continue down this path and use the primes 2, 3, 5, and 31 to create a new number, this time we get 931, which also cannot be factored by any of the primes we used to create it. as it turns out, 931 is not a prime. it can be divided by both 7 and 19. but guess what, we've just discovered two new primes. so even if the output of euclid's formula is not itself a prime number, any of its factors

so then euclid goes one step further. and that's the point. having identified the primes, we can now ask questions like, how many of them are there? and what euclid proved is that there are an infinite number. so let's see how he did it. euclid's proof of the infinitude of primes shows that if we multiply together any finite collection of primes and then add 1, the resulting sum is not divisible by any of the primes that we start with. for example, multiply the prime numbers 2, 3, and 5 and then add 1. the result is 31, a number which can't be divided by either 2, 3, or 5. but in fact, 31 is itself prime, so we've discovered a new prime number! now, if we continue down this path and use the primes 2, 3, 5, and 31 to create a new number, this time we get 931, which also cannot be factored by any of the primes we used to create it. as it turns out, 931 is not a prime. it can be divided by both 7 and 19. but guess what, we've just discovered two new primes. so even if the output of euclid's formula is not itself a prime number, any of its factors

for kevin euclid and allison read it was a charity event in a bid for youth is.servicemen and women. this is very nice, and on the heels of the yankee series. >> in the last couple of weeks we start paying attention a little bit more. it is something a look at after the game. we're not letting that bother us, we cannot control what they do. >> bad news for the tigers. miguel cabrera out early against the blue jays with a sore ankle nothing serious. justin verlander did not beat the jays today, but the jays couldn't beat the tigers, either. bottom eleven, alex ah-vee-la base hit to right field brings in quentin berry. tigers finish off the sweep, 3-2, remain within a game and a half of the white sox, who had the day off. sox have gotten a big lift lately from an old favorite. dewayne wise was released by the yankees, picked up by the sox and he hasn't stopped hitting since. sox fans remember d-wise more for his defense - 2009. mark buehrle working on that perfect game in the ninth against tampa bay and wise saved the day at the wall. hard to imagine this guy was a

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