Project Euler Forum

If you add 2,4,6..... To these four prime numbers then you will get a series of primes 5- 5,7,11,17,25 11-11,13,17,23,31,41,53,67,83,101,121 17- 17,19,23,29,37,47,59,73,89,107,127,149,173,199,227,257,289 41- 41,43,47,53,61,71,83,97,113,131,151,173,197,223,251,281,313,347,383,421,461,503,547,593,641,...

As i have learnt sieving has limits. What if i want to factor a 20 digit number or say a 50 digit number. How would I do it?

Thank you very much

You mean if n=4 then following pi sequences can be created
4,2,1 and 4,2 and only one of them have one not prime, k=c(u), which is 4,2.
Is it? Correct me if I'm wrong.

If that's correct help me with last doubt. Who will choose values of n and k?

I didn't understand the following line :-
Let p(n,k) be the number of π sequences u for which $u_0$ ≤n and c(u)=k .

can you please clear it to me with a suitable example?

euler wrote: ↑Sun Sep 10, 2017 11:51 am @S_r: Are you requiring a list of all the divisors or do you need to know the number of divisors / sum of divisors?

Hi,
I want to know how to get all the prime factors of a number.
Recently I have learnt sieving from Muthu, which is an excellent method. still looking for more efficient methods.

To be specific the problem requires all the factors and not only the prime ones so-
1 how would it help by taking the sqrt(n)
2 all factors are needed(not only the primes)
3 i dont know how to use sieve

And finally in india the power supply has never run for a day continuously

The only method of factoring that i know is trial division. When i used it in solving a problem i got to know how bad it is. As the number increases the number of factors increses too. Even after calculating for two hours the number reached was not even one fourth of destined number. Help me please....

Anything on number theory? Which branch do you like?

Thanks

Which books would you prefer if i want to learn about number theory, factoring, different methods of finding primes and a great book on maths?

Good for you. Which language do you use?