Interesting idea on factoring

[mgb]

This is interesting but how does he find Nf(N)?

https://mae.ufl.edu/~uhk/QUICK-SEMI-PRIME-FACTORING.pdf

[ewmayer]

Originally Posted by mgb

This is interesting but how does he find Nf(N)?

https://mae.ufl.edu/~uhk/QUICK-SEMI-PRIME-FACTORING.pdf

Yes, exactly that "how" bit seems curiously absent from the manuscript. It's only interesting if his "how" is asymptotically faster than brute force. We read "We want here to combine all this information to indicate a quick (but brute force) approach to factoring large semi-primes." Uh, pic one or the other - if it's brute force it won't be "quick".

Smells a lot like crankery, but let's have a look:

1. He mentions previous work leading up to the present treatise, but provides no references or links to same.

2. The very first formula he gives here features a function sigma(n) on the RHS. he does not define that function.

3. He starts with the semiprime to be factored N = p*q, and his function f(N) featuring the mystery sigma-function turns into just f(N) = (p+q)/N, thus N*f(N) = p+q, the sum of the 2 primes which are sought. Next we come to the "and then a miracle occurs" part of the manuscript, in form of his first example:

"Let us demonstrate the procedure for several examples involving larger semi-primes. We begin with the eight digit semi-prime N=21428053. It produces an Nf(N) of 9334."

He does not say *how* "it produces" the sum of the 2 prime factors of N, he just gives the latter. As do all his subsequent "impressively larger semiprime" examples. Give me the sum and product of the p and q for any RSA challenge number or other such semiprime, of course I can quickly find p and q.

So if anyone can dig out any of this guy's "several earlier articles" which hopefully details the "it produces" part of the algorithm, by all means post it here.

[Uncwilly]

Originally Posted by ewmayer

So if anyone can dig out any of this guy's "several earlier articles" which hopefully details the "it produces" part of the algorithm, by all means post it here.

I looked him up. He is a retired fluid flow physics prof. Note, that the work is ~6.5 years old and not well known. Didn't see any previous math works (I didn't look up on G scholar).

[sdbardwick]

Author's school homepage: https://mae.ufl.edu/~uhk/ if somebody wants to start researching.

[Viliam Furik]

I visited the site RIC’S TECH BLOG he pointed to and found out the sigma function is the divisor function (wiki). But in order to know the sigma, you have to know divisors first, but you don't know them yet...

Edit: In order for this method to work, you have to know the factors in order to compute them... It reminds me of a joke about dried water my grandfather introduced me to: "Few soldiers go on a mission to a desert, and soon they run out of water. They remember that their army scientists have just made a new discovery, powdered water, and they have a kilogram of it each. When they get to the manual, on how to use it, the first step is to pour water into the cup with the dried water in it..."

It's kind of a dry joke (pun intended) but hides a deep philosophical thought about such a thing because it should turn liquid in contact with itself because it is still water, only dried.

[ewmayer]

Originally Posted by Viliam Furik

I visited the site RIC’S TECH BLOG he pointed to and found out the sigma function is the divisor function (wiki). But in order to know the sigma, you have to know divisors first, but you don't know them yet...

Thanks - so the ingenious new factoring algorithm is, as I surmised, BASED ON PRIOR KNOWLEDGE OF THE FACTORS. Genius! That Sidney Harris cartoon I linked to really is apt.

[mgb]

Originally Posted by ewmayer

Yes, exactly that "how" bit seems curiously absent from the manuscript. It's only interesting if his "how" is asymptotically faster than brute force. We read "We want here to combine all this information to indicate a quick (but brute force) approach to factoring large semi-primes." Uh, pic one or the other - if it's brute force it won't be "quick".

Smells a lot like crankery, but let's have a look:

1. He mentions previous work leading up to the present treatise, but provides no references or links to same.

2. The very first formula he gives here features a function sigma(n) on the RHS. he does not define that function.

3. He starts with the semiprime to be factored N = p*q, and his function f(N) featuring the mystery sigma-function turns into just f(N) = (p+q)/N, thus N*f(N) = p+q, the sum of the 2 primes which are sought. Next we come to the "and then a miracle occurs" part of the manuscript, in form of his first example:

"Let us demonstrate the procedure for several examples involving larger semi-primes. We begin with the eight digit semi-prime N=21428053. It produces an Nf(N) of 9334."

He does not say *how* "it produces" the sum of the 2 prime factors of N, he just gives the latter. As do all his subsequent "impressively larger semiprime" examples. Give me the sum and product of the p and q for any RSA challenge number or other such semiprime, of course I can quickly find p and q.

So if anyone can dig out any of this guy's "several earlier articles" which hopefully details the "it produces" part of the algorithm, by all means post it here.

You caught all the essential points. When I read it first I thought this guy was really on to something but then I thought (p + q)/N? Where did he get p and q? He's pulling rabbits out of hats here. I guess this was written to impress someone who is not up to speed on these matters!

[mgb]

Originally Posted by Viliam Furik

When they get to the manual, on how to use it, the first step is to pour water into the cup with the dried water in it..."

It's kind of a dry joke (pun intended) but hides a deep philosophical thought about such a thing because it should turn liquid in contact with itself because it is still water, only dried.

LOL Great analogy.

[ewmayer]

Originally Posted by Viliam Furik

Edit: In order for this method to work, you have to know the factors in order to compute them... It reminds me of a joke about dried water my grandfather introduced me to: "Few soldiers go on a mission to a desert, and soon they run out of water. They remember that their army scientists have just made a new discovery, powdered water, and they have a kilogram of it each. When they get to the manual, on how to use it, the first step is to pour water into the cup with the dried water in it..."

Ha - when I was in 8th grade we were tasked with a "new product invention" sales-pitch assignment. My breakthrough product was just what your grampa used: dehydrated water. To demonstrate, I sat at front of the class behind the teacher's desk in her seat, used baking soda for the dehydrated water and white vinegar for the "just add water" bit. The resulting fizzy mixture overflowed the beaker I was using and flooded the teacher's desk. Ah, good times.

[mgb]

Originally Posted by ewmayer

Ha - when I was in 8th grade we were tasked with a "new product invention" sales-pitch assignment. My breakthrough product was just what your grampa used: dehydrated water. To demonstrate, I sat at front of the class behind the teacher's desk in her seat, used baking soda for the dehydrated water and white vinegar for the "just add water" bit. The resulting fizzy mixture overflowed the beaker I was using and flooded the teacher's desk. Ah, good times.

Our science teacher once showed us how phosphorus fizzes in water. Then we got a new science teacher and we asked him to do the phosphorus trick for us. He put in WAY too much and it exploded with awesome force filling the classroom with fumes.

[kriesel]

https://mae.ufl.edu/~uhk/MATHFUNC.htm is massive and a little behind the times in regard to Mersenne prime discoveries. "One of the latest Mersenne primes which has been verified by computer is the 9.8 million place number (2^32582657-1) . We discuss at PRIMES some properties of prime numbers and discuss how one might obtain even larger primes by a known extention of the Mersenne postulate that 2^p -1 is prime for certain prime numbers. So far the first 44 Mersenne primes have been found. A finacial award of 100K is posted on the internet for anyone finding the first p with more than ten million digets." That's a copy/paste, not transcription typos.

The next bit is odd. "In playing around with prime numbers, I noticed that the complex function F(n)= n exp(i Pi n/4) places all prime numbers along the intersection of the Archimedes spiral defined by this F in the complex plane and the 45 degree diagonal lines(see attached PRIME-NUMBER-PATTERN.jpg). Perhaps such a geometrical interpretation will in the future be of aid in determining the prime or non-primeness of large integers without requiring extensive divisions by smaller prime numbers." Isn't every odd integer n on those diagonals, and evens on the vertical or horizontal, and shouldn't that be trivially obvious to someone teaching what he does? And trivial compared to using the wheel to discard composite factor candidates factorable by any of multiple small factors?

In https://mae.ufl.edu/~uhk/PRIME-NUMBERS.pdf there's "Computer evaluation programs to check out Mersenne primes are much simpler than those using the Eratosthenes Sieve" so I guess George, Ernst, and all the rest of us have wasted our time, and all those megabytes of careful processor-type-specific tuned code is just fluff. The bottom of this file, which is dated 2008, is also a few years behind the times, since https://www.mersenne.ca/exponent/2147483647 was factored years ago. Easily, as it turns out; 4 prime factors were found.
His number fraction is defined at https://mae.ufl.edu/~uhk/NUMBER-FRACTION.pdf.
To evaluate it requires complete prime factoring of the large number. He typically relies on MAPLE for that feat.

The other root web page Ric's tech blog is at https://mae.ufl.edu/~uhk/TECH-BLOG.html and includes a reference to RSA cryptography. https://mae.ufl.edu/~uhk/RSA.pdf and a page using his number fraction approach https://mae.ufl.edu/~uhk/PRIME-OR-COMPOSITE.pdf
There's also his attempt at number theory in which Goldbach's conjecture seems misstated (otherwise 2+3=5 which is odd would disprove it). https://mae.ufl.edu/~uhk/NUMBER-THEORY.pdf
He's pretty close to the mark on the national debt prediction versus time, and the recent coronavirus-related massive spending bills establish approximate error bars, although the prediction of onset of hyperinflation seems premature, and the claim that tangible property such as precious metals or real estate become worthless in that scenario seems odd. https://mae.ufl.edu/~uhk/NATIONAL-DEBT.pdf
I don't know what to make of https://mae.ufl.edu/~uhk/FACTORING-N-USING-k.pdf
There are more, but they seem to me to be revisiting nearly the same ground after a while. The end of his tech blog includes some Coronavirus related material, and a prediction for 2 million more deaths worldwide by late April than occurred yet per the worldometer site.