[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 286

[Sceptic Philozoff]

No, they are not, even if you list all the mathematicians who have done higher arithmetic. The problem is in the nature of an existence theorem. If you do find these 15 numbers, you cannot prove that for any other 15 prime numbers forming the progression, the difference is still at least 30000.

[Vladimir Gomonov]

Let's start small. I can prove it's at least 15. Who's bigger?

[Sceptic Philozoff]

30030 = 2*3*5*7*11*13. Who's next?

[Vladimir Gomonov]

That's exactly what I was hinting at. Let's do the next one.

Mathemat >>:
30030 = 2*3*5*7*11*13. Кто дальше?

[richie]

Mathemat писал(а) >>
30030 = 2*3*5*7*11*13. Who's next?

Are we talking about the difference in progression? The difference should be >30000. Or am I misunderstanding something.

[Vladimir Gomonov]

MetaDriver >>:
Давай следующую.

No. You'd better prove it first.

[Vladimir Gomonov]

Richie >>:

Речь идёт о разности прогрессии? Разность должна быть >30000. Или я что-то не понял.

You got that right. :)

[Sceptic Philozoff]

Richie, the difference must always be at least 30000 - and nothing else. If you want, find it and post it here for illustration.

I haven't solved the problem of 15 prime yet :) Have you solved it, MetaDriver?

[Vladimir Gomonov]

Mathemat >>:
Задачку о 15 простых я еще не решил :)

Me too. I mean, the intuition is that the answer is the one, the question is in the proof. Let's speculate. interesting.

So with fifteen (> 15) there is no question. Let's think further.

// New problem taken note of.

[Sceptic Philozoff]

I'll take my time, it's urgent. I'll try to figure it out. The problem should be simple, actually.
And show me, Volodya, how you proved that the difference can't be equal to, say, 14.
All right, go to sleep. Morning will be better in the morning.
P.S. Maybe in the problem of 15 prime numbers it is enough not simplicity of numbers, but pairwise mutual simplicity?