Twin Prime Conjecture Proof: Shubhankar Paul
Twin Prime Conjecture Proof: Shubhankar Paul
Twin Prime Conjecture Proof: Shubhankar Paul
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Twin Prime Conjecture Proof
Similarly. we can find for other prime numbers which on tester with designation Application Consultant. Worked in IIT Bombay for 3
months as JRF.
division of 30(n+1) gives 1 as remainder.
Now as we see the prime number is increasing (property of
natural number) so the common difference will also increase.
Now we need to find numbers which are not part of these
series taken simultaneously.
As the prime number series diverges as it goes on increasing
then there must be some integers which are not part of these
series. So that we can find n and substitute to get a twin prime
generator. Once twin prime generator is found then twin
primes can be found.
If the numbers which gives remainder 1 is called set {n} =
{7}{11}{13}.... then {n} must be subset of {Z} the set of
integers. {Z}-{n} gives the n's for which 30 + 30n is a
generator of twin prime. Exclude the numbers which gives 1
as remainder with quotient 1 because they are prime.
Obviously {z}-{n} is non-empty because 1 is an element of
the set as 59 and 61 twin prime itself. And {Z}-{n} is infinite
as the series of {n} continues to go on so we will find
corresponding {Z}-{n}.
This similar case also goes with the numbers 12 + 30n and 18
+ 30n.
II. RESULT
Twin primes are infinite.
III. CONCLUSION
The Twin Prime Conjecture is true.
REFERENCES
1. Lou S. T., Wu D. H., Riemann hypothesis, Shenyang: Liaoning Education
Press, 1987. pp.152-154.
2. Chen J. R., On the representation of a large even integer as the sum of a
prime and the product of at most two
primes, Science in China, 16 (1973), No.2, pp. 111-128..
3. Pan C. D., Pan C. B., Goldbach hypothesis, Beijing: Science Press, 1981.
pp.1-18; pp.119-147.
4. Hua L. G., A Guide to the Number Theory, Beijing: Science Press, 1957.
pp.234-263.
5. Chen J. R., Shao P. C., Goldbach hypothesis, Shenyang: Liaoning
Education Press, 1987. pp.77-122; pp.171-205.
6. Chen J. R., The Selected Papers of Chen Jingrun, Nanchang: Jiangxi
Education Press, 1998. pp.145-172.
7. Lehman R. S., On the difference (x)-lix, Acta Arith., 11(1966). pp.397
410.
8. Hardy, G. H., Littlewood, J. E., Some problems of patitio numerorum
III: On the expression of a number as a
sum of primes, Acta. Math., 44 (1923). pp.1-70.
9. Hardy, G. H., Ramanujan, S., Asymptotic formula in combinatory
analysis, Proc. London Math. Soc., (2) 17 (1918).
pp. 75-115.
10. Riemann, B., Ueber die Anzahl der Primzahlen unter einer gegebenen
Groe, Ges. Math. Werke und
Wissenschaftlicher Nachla , 2, Aufl, 1859, pp 145-155.
11. E. C. Titchmarsh, The Theory of the Riemann Zeta Function, Oxford
University Press, New York, 1951.
12. Morris Kline, Mathematical Thought from Anoient to Modern Times
Oxford University Press, New York, 1972.
13. A. Selberg, The zeta and the Riemann Hypothesis, Skandinaviske
Mathematiker Kongres, 10 (1946).
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