Math Is Fun Forum

Whatever, but I consider it cool!
I don't know such advanced stuffs, so may not be able to understand how you derived it. I have heard only 'Riemann hypothesis', is it the same Riemann in 'Riemann Rearrangement'?
You are a polymath, I am a wannabe

Hi Charlie,

Not true, only 101 is prime.
There is no easy pattern or equation to find prime numbers, though there is a prime number theorem: http://en.wikipedia.org/wiki/Prime_number_theorem

Anyway, what's the correct question?
If I assume the question to be : "Find two numbers that, if multiplied, would generate a 400-digit number.", then one possible answer would be

Thanks ganesh,

Yes, we are all here to enjoy the math!

I was checking the difference. On seeing its order of magnitude, I felt like that...
Thanks for the link.

Hi 4DLiVing,
I can't say for now. It may be possible to derive the next line, like finding numbers in bell triangle or pascal triangle, but a closed form may not exist.

Hi bobbym,
Has anyone proved that a closed form cannot exist for recurrences like Stirling numbers? Is there any approximation like stirling's approximation for n!  ?

Yes, I went exactly to those two pages before replying
Thanks...

Hi bobbym,

I'll tell how I calculated it.
When race results in -
1: No tie - i.e. [1 2 3] - the possibility is 3! ways
2: All tie - [1 1 1] - 1 way
3: 2 finish second -[1 2 2] - 3!/2! = 3 ways
4: 2 finish first - [1 1 2] - 3!/2! = 3 ways.

Hence totals to 13 ways. I hope I'm clear.

Thanks... you helped me to know the application of exponential generating function.

Last one thing to ask,
what if I want the chosen number to begin with 1?

Is this the generating function:

Oh, I haven't dealt with multisets I did not know it was called a multiset... The books I have seen, as I remember, did not have the topic of multisets under generating function...

So, if I need to know the no. of 5-digit numbers, is it (co-efficient of x^5) * (5!) ?