Bernoulli Number's conjeture?

  • Thread starter Damidami
  • Start date
  • Tags
    Bernoulli
In summary, the Bernoulli Number's conjecture is a mathematical hypothesis stating that all Bernoulli numbers with odd denominators are equal to 0, except for the first one which is equal to 1. It has important applications in number theory and other branches of mathematics and is closely related to the Riemann zeta function. While it has not been proven, it has been verified for many cases and is considered to be true by many mathematicians. If proven, it would have significant implications and there are ongoing efforts to prove it using various techniques, including computer assistance.
  • #1
Damidami
94
0
Is this a known bernoulli number conjeture/theorem?:
The denominators of B_n (when expressed as an irreducible fraction), doesn't contain as a factor powers of prime numbers (ex. isn't divided by 5^2)

Example:

B_2 = 1/6
6 = 2*3

B_4 = -1/30
30 = 2*3*5

B_{24} = -236364091/2730
2730 = 2*3*5*7*13

I know Ramanujan proved that the denominator contain 2 and 3 as a factor one and only once, but I hadn't heard that any prime on the factorization of the denominator happens only once.
 
Physics news on Phys.org
  • #2
Nevermind.

http://en.wikipedia.org/wiki/Von_Staudt%E2%80%93Clausen_theorem"

Aditional information is welcome.
 
Last edited by a moderator:

1. What is the Bernoulli Number's conjecture?

The Bernoulli Number's conjecture is a mathematical hypothesis made by mathematician Jacob Bernoulli in the 18th century. It states that all Bernoulli numbers (a sequence of rational numbers) with odd denominators are equal to 0, except for the first one which is equal to 1.

2. Why is the Bernoulli Number's conjecture important?

The Bernoulli Number's conjecture is important because it has many applications in number theory, algebra, and other branches of mathematics. It is also closely related to the Riemann zeta function and is used in the study of prime numbers and other important mathematical concepts.

3. Has the Bernoulli Number's conjecture been proven?

No, the Bernoulli Number's conjecture has not been proven. It remains an open problem in mathematics and has been a topic of research for many mathematicians over the years. However, it has been verified for many specific cases and is considered to be true by many mathematicians.

4. What are some potential consequences if the Bernoulli Number's conjecture is proven?

If the Bernoulli Number's conjecture is proven, it would have significant implications in number theory and other areas of mathematics. It would also lead to a better understanding of prime numbers and other key mathematical concepts.

5. What are some current efforts to prove the Bernoulli Number's conjecture?

There are many ongoing efforts to prove the Bernoulli Number's conjecture, including various approaches using algebraic, analytic, and probabilistic techniques. Some mathematicians have also attempted to prove the conjecture using computer-assisted methods. However, as of now, the conjecture remains unproven.

Similar threads

MHB How can we use hints to prove divisibility of Fibonacci numbers?
    • General Math
Replies
1
Views
1K
A Anti-dual numbers and what are their properties?
    • Linear and Abstract Algebra
Replies
1
Views
914
Comp Sci Finding Cousins of Giuga Numbers: Can You Solve This Prime Number Puzzle?
    • Engineering and Comp Sci Homework Help
Replies
32
Views
3K
MHB -c5.LCM and Prime Factorization of A,B,C
    • General Math
Replies
3
Views
550
Prove ##|\{ q\in\mathbb{Q}: q>0 \} |=|\mathbb{N}|##.
    • Calculus and Beyond Homework Help
Replies
3
Views
544
I Math Myth: A prime is only divisible by 1 and itself
    • General Math
Replies
4
Views
917
I I think I've hit upon a very easy proof of impossibility of quintic
    • Linear and Abstract Algebra
Replies
2
Views
953
MHB Apc.1.1.13 what is the prime factorization of 30,030
    • General Math
Replies
3
Views
766
Determine whether the integer 701 is prime by testing?
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
I Union of Prime Numbers & Non-Powers of Integers: Usage & Contexts
    • General Math
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top