4 ms·
Nope :) Consider the number 1000000! + 1 (one million factorial plus 1). 1000000! + 2 is divisible by 2. 1000000! + 3 is divisible by 3. ... 1000
by prezjordan 13y ago
Nope :) Consider the number 1000000! + 1 (one million factorial plus 1).
1000000! + 2 is divisible by 2.
1000000! + 3 is divisible by 3.
...
1000000! + 1000000 is divisible by 1000000.
Here we have a gap of 999999 numbers, none of which are prime.
- undershirt 13y agoThat is a neat proof :D
- atmosx 13y agoWeird, I just read about this exact example yesterday in the "music of primes" by Markus De Sautoy. I'm not sure though if it was the German Siegel or the Norwegian guy (Sebel or something) who also end up to Princeton to figure it out, or maybe it was known already by Euler's time :-) Neat proof indeed.
- prezjordan 13y agoI first read it a few years back in Excursion's in Number Theory [0]. Super approachable (and short!), I read it in high school with only a little bit of calculus knowledge. [0]: http://www.amazon.com/Excursions-Number-Theory-Dover-Mathematics/dp/0486257789 http://www.amazon.com/Excursions-Number-Theory-Dover-Mathema...