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OT: Cool math fact, about prime numbers.

LionJim

LionJim

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Leo Ridens said:
LionJim, I appreciate the "purity" of mathematics, and the gerneral approach of mathematicians, but you must admit that physicists sometimes create new areas of mathematics by pursuing physics. Newton and calculus are well known to everyone, but more recently, string theory opened new areas of mathematics unforeseen by "pure" mathematicians, and theoretical physicist Edward Witten won the Fields Medal in 1990 for his groundbreaking mathematics. Give us poor physicists some small crumb of credit where due, OK? ;)
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Yeah, Ed Witten rules.
 
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LionJim

LionJim

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Oct 12, 2021
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Leo Ridens said:
LionJim, I appreciate the "purity" of mathematics, and the gerneral approach of mathematicians, but you must admit that physicists sometimes create new areas of mathematics by pursuing physics. Newton and calculus are well known to everyone, but more recently, string theory opened new areas of mathematics unforeseen by "pure" mathematicians, and theoretical physicist Edward Witten won the Fields Medal in 1990 for his groundbreaking mathematics. Give us poor physicists some small crumb of credit where due, OK? ;)
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Another example? Feynman’s concept of Sum over Histories.

 
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LionJim

LionJim

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I have always been good at math but math wasn’t my passion growing up, literature was. Penn State was a bad fit for me, deaf; I got into math only because it was the one subject where I could take my own notes, imagine that. It was absolutely a deludedly stupid move for me to go to Penn State and I absolutely love how things worked out. Charmed life, believe you me.
 
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IrishHerb

IrishHerb

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LionJim said:
#subjectlinesmatter

Euclid proved that if S is any finite set of prime numbers then there is some prime number p which is not contained in S. Ergo, there are infinitely many primes. Nice proof, easy to understand.

Now:
8, 9, 10 are three consecutive non-primes.

32, 33, 34, 35, 36 are five consecutive non-primes.

212, 213, 214, 215, 216, 217, 218 are seven consecutive non-primes.

It’s an easy algorithm. To illustrate by using the last example, multiply 2, 3, 5, and 7 together to get 210 and then add 2, 3, 4, 5, 6, 7, 8 in succession to 210. 212 is divisible by 2, 213 by 3, 214 by 2, 215 by 5, 216 by 2, 217 by 7, 218 by 2. So, all non-primes.

So if you take any prime p, you can find a run of p consecutive non-primes. Since there are infinitely many primes, if X is the number of seconds from the Big Bang (13 billion years ago) to the moment I post this, you can find a run of X consecutive non-primes. Every second since the Big Bang, start with a non-prime the next number is itself a non prime. And there are infinitely many primes coming up afterwards. That blows my mind. Infinity is big.

YMMV. Thanks for indulging me. Now, off to the gym!
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Thanks Jim, I've been starving for some math since Christmas. Gotta get some more soon.
 
IrishHerb

IrishHerb

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LionJim said:
So did both Heisenberg and Feynman, they would have been great mathematicians but kept asking where the applications were. No mathematician worth his salt asks that question.

Here’s an easy-to-explain open problem: the Twin Primes Conjecture. There are infinitely many prime numbers, as we have known for 2300 years. Twin primes are pairs p and p+2 which are both prime. For example, 3 & 5, 5 & 7, 11 & 13, 17 & 19, 29 & 31, you get the idea. Question: are there infinitely many pairs of twin primes? Nobody knows, and every single day someone is trying to prove it one way or the other. Zero practical applications that I can think of.
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You never know. A lot of math is discovered for its own sake. But years ago when my daughter was at Columbia studying for her PhD ... in a purely theoretical class (for got exactly what it was), one of her classmates or was just sitting in, was an Economics major .... and one day during class he started jumping up and down and getting all excited ... after class she asked him what was going on, and he said that theoretical math the professor was lecturing on apparently applied to some economic problem he was struggling with.

Similar to that noon time lecture at our school by that guy from NSA ... he was talking about self correcting codes. Said that the math that is used was discovered and proved about 100 years before it was applied to self correcting codes.
 
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step.eng69

step.eng69

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Lion Jim,
Please, let the baby sleep 💤 💤 💤,
Is the Baby's middle name Constant?

Make sure the baby remembers the "+C"😧
 
Grant Green

Grant Green

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LionJim said:
#subjectlinesmatter

Euclid proved that if S is any finite set of prime numbers then there is some prime number p which is not contained in S. Ergo, there are infinitely many primes. Nice proof, easy to understand.

Now:
8, 9, 10 are three consecutive non-primes.

32, 33, 34, 35, 36 are five consecutive non-primes.

212, 213, 214, 215, 216, 217, 218 are seven consecutive non-primes.

It’s an easy algorithm. To illustrate by using the last example, multiply 2, 3, 5, and 7 together to get 210 and then add 2, 3, 4, 5, 6, 7, 8 in succession to 210. 212 is divisible by 2, 213 by 3, 214 by 2, 215 by 5, 216 by 2, 217 by 7, 218 by 2. So, all non-primes.

So if you take any prime p, you can find a run of p consecutive non-primes. Since there are infinitely many primes, if X is the number of seconds from the Big Bang (13 billion years ago) to the moment I post this, you can find a run of X consecutive non-primes. Every second since the Big Bang, start with a non-prime the next number is itself a non prime. And there are infinitely many primes coming up afterwards. That blows my mind. Infinity is big.

YMMV. Thanks for indulging me. Now, off to the gym!
Click to expand...
LJ, possibly of some interest to you....
Math Rock
 
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