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Does anyone think that factoring will be shown to be "fractal" in nature, following the work of Ken Ono. Are there patterns in composite numbers, as yet unknown, that make factoring easier?
Dragonfall said:If I interpret your question correctly: no, they don't, because of the prime number theorem.
Goongyae said:The amazing thing is d(n) can be computed recursively:
d(n) = d(n-1)+d(n-2)-d(n-5)-d(n-7)+d(n-12)+d(n-15)-...
except if you get d(0) on the right hand-side, you must put in the number n itself.
Well this is rather interesting and more than a bit related to the topic of this thread...Raphie said:In other words, all primes greater than 3 are constructible in the following manner: sqrt (24*(Generalized Pentagonal Number_n) + 1), a fact which might naturally lead one to ask: Is this in some manner related to the Dedekind eta function? Conversely, working backwards, then (p^2 - 1)/24 for p > 3, will always be a Generalized Pentagonal Number
Goongyae said:There is a very interesting recursive property that can be used to deduce if a number is prime or not.
Check out this stuff from Euler: http://www.math.dartmouth.edu/~euler/
English translation: http://lambentresearch.com/euler/e175.pdf
Ken Ono is a renowned mathematician and professor at Emory University. He is known for his groundbreaking work in the field of number theory, specifically in the area of factoring numbers.
Ken Ono's work has greatly advanced our understanding of factoring large numbers, which is crucial for encryption methods and cybersecurity. His research has also led to the development of more efficient factoring algorithms.
Factoring is the process of breaking down a number into its prime factors. This is important because it helps us understand the properties of numbers and can also be used in cryptography to keep information secure.
Ken Ono has been interested in mathematics since a young age and was drawn to the challenge of factoring large numbers. He also realized the importance of factoring in real-world applications and wanted to contribute to this field of study.
Ken Ono's work has opened up new avenues for research in factoring. Some potential developments include finding more efficient algorithms for factoring large numbers, exploring the connections between factoring and other areas of mathematics, and applying factoring techniques to other fields such as physics and computer science.