A Radical Approach to Integer Factorization

1. Algorithm Intfact:
Route Through
Riemann Zeros
SUBHENDRA BASU

2. Route Through the
Riemann Zeros
To know more about the Riemann Zeros:
https://en.wikipedia.org/wiki/Riemann_zeta_function
http://www.dtc.umn.edu/~odlyzko/zeta_tables/zeros2

3. The Approach to
Factorizing Integers
When the Universe started , at that instant the Riemann
Zeros came into existence and there are infinite number
of zeros. And each zero extends infinitely.
We all (the physical universe) is composed of fragments
of these zeros at an abstract level

4. Testcase: 125
Π: 3.1415926535897932384626433832795028..
Riemann Zeros
Z1:4.134725141734693...(Match @1)
Z2:1.022039638771554...(Mismatch @6)
Z3: 5.01085758014568876321379099256282181865
(Mismatch @ 8)

5. 125, Contd.
Π: 3.1415926535897932384626433832795028..
Z4: 0.4248761258595....(Mismatch @9)
Z5: 2.935061587739(Mismatch @9)
Z6: 7.58617815 (Match @5)
Note that this is out of sequence match, the original
number was 125, in binary we have: "11..."

6. 125 contd.
The match occurs at an interval of 4 zeros
Π[4] = 5 (R2L)
E[4] = 2 (L2R)
We have not yet completed the factorization

7. 125 Contd.
Π: 3.1415926535897932384626433832795028..
Z7: 0.91871901214749 Mismatch @9
Z8: 3. Mismatch @3
Z9: 8.005150881167159727942 Mismatch @2(not
between 1 and 5 previously)
Z0: 9.7738324776 Match @2

8. 125 Contd
The last match occurs at interval of 8 zeros from Z1
Π[8] = 5 (L2R)
E[8] = 2 (R2L)
In Binary: "110..." (alternating digits in the number to be
factored encoded as 1 and 0)
In principle , Factorization is finished. But we continue to
demonstrate the factor in binary.

9. 125, Contd., Z11
3.141592653589793238462643383279502884197169
2.970321477714460644147296608880990063825017
πcontd.: 39937510582097494
Z11, cont.:8888212247799 ( mismatch at 9)

10. 125, Contd., Z12
3.141592653589793238462643383279502884197169
6.44 Mismatch at 4
Z13:
9.34 Mismatch at 4
Z14:
0.831 Mismatch @1 (out of sequence)

11. 125, Contd.
5.112544048081606660875054253183705 (repeat
match,1)
match 1521
Binary, "1100...
3.14159265358979323846264338
7.079810529494173 Mismatch @3

12. 125, Contd.
3.14159265358979323846264338
9.5464017111739792 (Match @2)
Match: 15212
Binary : 11001
This is based on the assumption that we assign truth
values 0 and 1 to alternating digits in the number to be
factored.

13. 125, Factored
Binary 11001 is 25 in decimal
Hence 25 is a factor

14. Conclusion
The solution is subject to continuous refinement (we can
find more refined ways of finiding the factors) but the
basic premise remains the same as mentioned in Slide
#3.
Also there is not one way of achieving the same solution.
In the coming days, its possible, I could present a
approach best suited for computer implementation. We
can program this approach as well but am always in the
lookout for better approaches.

15. Thank You
Feedback:
basu.subhendra@outlook.com