Review

, Volume: 14( 4)

• View PDF
• Download PDF

How to Know All Prime Numbers and All Numbers Divisible with a Prime Number Only: Seven

*Correspondence:

Filiberto MarraDepartment of Mathematics, Via Luigi Meneghetti 1, 31100 Treviso TV, Italy; E-mail: filiberto.marra@gmail.com

Abstract

This study on prime numbers presents a method that allows us to know divisible numbers without performing complex calculation system using examination of composition of number s. Example 143=11 × 13, 493=17 × 29. I can know all prime numbers with this examination of composed number number.

Keywords

Prime numbers numbers; Divisible numbers

About the Study

Before I start proving that the idea of knowing all divisible and prime numbers with only one number is true, let me tell you about a dream I had one night.

In the dream, a musician was answering a question from a person who was present in the dream. He asked the musician: Why are there seven notes? The musician replied by pointing out that with seven notes you could create all kinds of music present in many life situations: Joy, pain, sadness, study, etc., etc.

He affirmed that music is harmony and suddenly he started talking about the Riemann hypothesis. He hoped that someone would solve this hypothesis and be able to demonstrate harmony between the numbers. He said that prime numbers contributed with their presence to create a harmony that divisible numbers alone could not create.

I was surprised that my hypothesis appeared in the dream: Harmony between prime and divisible numbers which proved to be valid with this study. Prime numbers have an order and occupy the place left vacant by divisible numbers. Together they form a harmony.

Alone they cannot have harmony and create order.

The dream musician invited us to discover and make known the harmony between divisible and prime numbers in the set of numbers.

Since my first publication on prime numbers I had considered the hypothesis that the number seven was the fundamental number to be considered for the solution of the problem.

A few years have passed and now with the collaboration of Cristina Gabrieli, my neighbor, I have found the solution after analyzing some series of divisible odd.

I divide the result by seven and get a series of prime and divisible numbers.

It is not complicated to know the divisible numbers by the prime numbers 7, 11, 13 in the table: 49/7, 77/7, 91/7, 119/7, 121/11, 133/7, 143/11, 161/7, 169/13

Analysis of divisible numbers

In this study, I believe that the analysis of divisible numbers has not been given the importance it deserves.

Divisible numbers are considered numbers to be eliminated and perhaps few scholars have examined their composition.

I affirm and demonstrate that the solution of the problem of knowledge of prime numbers is solved by examining the composition of divisible numbers.

To simplify the search for divisible numbers, you can write a list of the first four divisible numbers for prime numbers 11 to 101 with the final number 1, 3, 7, 9.

I continue the table of divisible numbers after 1,211:

 

Composition of the divisible numbers of the table:

Divisible by 7: 203, 217, 259, 287, 301,3 29, 343, 371, 413, 427 are composed by the multiplication of the prime number

7 for prime numbers: 29, 31, 37, 41, 43, 47, 53, 59, 61.

I know 9 prime numbers.

Divisible by 11: 187, 209, 253, 319, 341, 407 are composed by multiplying the prime number 11 by the numbers

Primes: 17, 19, 23, 29, 31, 37 – I know 6 prime numbers.

Divisible numbers are composed of the multiplication of a prime number by other prime or divisible numbers.

It is a confirmation of the importance of the analysis of divisible numbers.

I continue the table of divisible numbers by writing only the result of the division by seven:

Analysis of numbers divisible by 11: 451, 473, 517, 583, 649, 671, 737, 781, 803, 869, 913, 979

They are composed of the multiplication of the prime number 11 by the prime numbers 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89.

I know 12 other prime numbers

Divisible numbers are composed of the multiplication of a prime number by other prime numbers and also divisible numbers.

The same for 13, 17, 19, 23, 29, 31. I continue the table after 1013.

Divisible by 11: 1067, 1111, 1133, 1177, 1199, 1243, 1331, 1397, 1441, 1507, 1529, 1573, 1639, 1661, 1727, 1793, 1727, 1793, 1837, 1859, 1903, 1969, 1991, 2057, 2101, 2123, 2167, 2189, 2299, 2321

They are composed of multiplying the prime number 11 by the prime numbers: 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 197, 199, 209, 211

I know 26 other prime numbers. Divisible numbers are composed of the multiplication of a prime number by other prime numbers.

The same for 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 etc.

I continue the table after 2393:

List of divisible numbers:

Per 11: 2431, 2453, 2497, 2519,2563,2629,2651,2717,2761, 2783, 2827, 2893, 2959, 2981, 3047, 3091, 3113, 3179, 3223, 3289, 3377, 3421, 3443, 3487, 3509, 3553, 3641, 3707, 3751, 3817, 3839.

They are composed of multiplying the prime number 11 by the prime numbers: (there can be numbers divisible by two prime numbers-2431:11,2431:13-I don't consider them) 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 3 31, 337, 347, 349, 353 I know of 24 other prime numbers.

I continue the table after 3893.

List of divisible numbers:

Per 11: 3949, 3971, 4037, 4103, 4147, 4169, 4213, 4279, 4301, 4367, 4411, 4433, 4477, 4499, 4609, 4631, 4741, 4763, 4807, 4829, 4873, 4939, 4961, 5027, 5071, 5093, 5137, 5203, 5269, 5291, 5357, 5401, 5423, 5489, 5533, 5599, 5687, 5731, 5753, 5797, 5819, 5863, 5951, 6017.

(Prime numbers for prime numbers: 11 × 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547). I know of 30 other prime numbers.

Confirmation of prime number search solution: multiplication of prime numbers by prime numbers.

Perhaps no one has analyzed the composition of divisible numbers and found the solution to easily know prime numbers. I continue the table:

List of divisible numbers:

Per 11: 6061, 6127, 6149, 6193, 6259, 6281, 6347, 6413, 6457, 6479, 6523, 6589, 6611, 6677, 6721, 6743, 6787, 6809, 6919, 6941, 7051, 7073, 7117, 7139, 7183, 7249, 7271, 7337, 7381, 7403, 7447, 7513, 7579, 7601, 7667, 7711, 7733, 7799, 7843, 7909, 7997

Prime numbers for prime numbers: 11 × 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727. I know of 28 other prime numbers. I continue the table:

List of divisible numbers:

Per 11: 8041, 8063, 8107, 8129, 8173, 8261, 8327, 8371, 8437, 8459, 8503, 8569, 8591, 8657, 8723, 8767, 8789, 8833, 8899, 8921, 8987, 9031, 9053, 9097, 9119, 9229, 9251, 9361, 9383, 9427, 9449, 9493, 9559, 9581, 9647, 9691, 9713, 9713, 9757, 9823, 9889, 9911, 9977, 10021, 10043

Prime numbers for prime numbers: 11 × 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911 is 27 prime numbers

In the table, the prime numbers from 8009 to 10039 remain.

As usual, divisible numbers are the result of prime number by prime number.

As they wanted to demonstrate: harmony between divisible and prime numbers.

I didn't write it but there are multiplications of two prime numbers up to 97 × 97=9409

Exercise: How to find divisible numbers and consequently prime numbers with numbers divisible only by the prime number seven, the king of numbers.

A table is built starting from the number 77, always adding 14. the table is similar to the first table but does not consider numbers that are divisible by 3.5 and all other prime numbers from seven onwards.

Considering only the numbers divisible by seven I find with this table the prime numbers from 11 to 479 with only addition easily eliminating numbers that are not divisible by seven. Continuous the table up to the prime number 1,301.

For those who read: Keep finding numbers that are only divisible by seven.

Example 9107+14=9121:7=1303 Prime number 9121+14=9135 no 9135+14=9149:7=1307 Prim 0 9149+14=9163 Divisible by 11, no 9163+14=9177 Divisible by 19 NO 9177+14=9191 no divisible by 13, 9191+14=9205 no divisible by 5– 9205+14=9219:7=1317 divisible by 3 – 9219+14=9233:7=1319 prime number.

Have a lot of patience

Also for the reader–find the prime and divisible numbers in the table

We ask you not to use pre-written lists of prime numbers and to explain what calculations are made to find the divisible numbers and consequently the prime numbers.

A help: in the magic table 209 is divisible by 11 – to 209 I add 11 × 10=110 or even first 1100 × 8=8800 and then 110 until I find: 209+8800=9009+(10 × 110=1100)=10109/11.