Radical Perfect Prime Numbers

Introduction to radical perfect prime numbers:
A radical perfect prime number is a symbol and it’s denoted as root of a number, the thought of a radical the root of a number can best be understood by first tackling the design of exponentiation, or raising a number to a given power. We point to a number raised to the nth power by writing xn. This expression denotes that we are multiplying x by itself n number of times. Example for radical perfect prime numbers, v5 =2.236, and v3 = 1.732. a radical perfect prime number is a number that has exactly 2 factors...1 and itself , and one thing is 1 is not a prime number ,so  that 2,3,5,7,11,13,17,19,23 etc  are all primes.

Examples for Radical Perfect Prime Numbers:

Addition for radical perfect prime number:

Example 1: Find the value of 2v3 +3 v3

Solution:

=v3 (2+ 3)
=5v3

Here the root is square root, only take the base are same so that we can add the roots easily.

So the result is =5v3

Example 2: Find the value of v11 +6 v23+5v11 +7 v23

Solution:

= v11 (1+5)+ v23 (6+7)

= v11 (6)+ v23 (13)

= 6 v11 + 13 v23

Here the root is square root, the base are same in different terms so that we can add the roots easily.

So the result is 6 v11 + 13 v23

Examples for different radical perfect prime numbers:

Example for square root:

v3 = 1.732

v5 = 2.23

v7 =  2.64

v11 = 3.31                              

Some other Examples for Radical Perfect Prime Numbers:

Multiplication for radical perfect prime numbers:

Example 1:

Solution:

To find multiplication of v3x . v1y    

= v(3 x y)            

=  v3x y   

The result is =  v3x y    

Both the radicals have an same index of two, so we are multiply mutually under one radical keeping the 2 as its index number.

Example 2:

Solution:

To find multiplication of v(23xy2). vy    

= v(23 x y3)            

= v(23 x y3)

The result is v(23 x y3)

Both the radicals have an same index of two, so we are multiply mutually under one radical keeping the 2 as its index number.


Factorization for Radical Perfect Prime Numbers Examples:

Example 1:

To find the value of v75

v75 = v5*3*3

= 3v5

Radical perfect prime factors for v75 = 3v5

So the result is in the form of prime numbers and radical.

Prime Consecutive Numbers

Introduction to prime consecutive numbers:

A prime number is an number that has only two factors and is divisible only by 1 and itself, and by no other positive integer.The first few prime numbers are 2, 3, 5, 7, 11,13, 17, 19, 23, 29, 31 and 37.

The consecutive number is nothing but adjacent numbers for example the consecutive numbers of 2 is 3, even consecutive number between 1 to 10 is 2,4,6,8,10.

The prime consecutive number are of rare as the prime number were not of adjacent values normally. But there are two prime numbers that is also consecutive. the two and three are the only prime consecutive numbers. Let us see more about  prime consecutive numbers.

Discussion on Prime Consecutive Numbers

More about prime numbers:

A prime number is a natural number larger than 1 which cannot be expressed as the product of two smaller natural numbers.

Prime numbers were first studied rigorously by the ancient Greeks. One of the first theorems they proved was

Euclid’s theorem (˜ 300 BCE) There are infinitely many prime numbers.

Arithmetic progressions of primes

As we mentioned earlier, we are still unable to detect several types of patterns in the primes. However, we have made recent progress on one type of pattern, namely an arithmetic progression a, a + r, . . . , a + (k - 1)r.

In particular, for any given k, the primes contain infinitely many arithmetic progressions of length k. This result builds upon a number of existing results; for instance, in 1939, van der Corput showed that the primes contained infinitely many arithmetic progressions a, a + r, a + 2r of length three.

2
2, 3
3, 5, 7
5, 11, 17, 23
5, 11, 17, 23, 29
7, 37, 67, 97, 127, 157
7, 157, 307, 457, 607, 757
. . . . . . .  .  . ..  .  .  .  .   .   .   . .  . .
I am planning to write more post on find the prime factorization of 36, multiplying and simplifying rational expressions. Keep checking my blog.

More Discussion on Prime Consecutive Numbers

Let us take an example of number of prime numbers from the 1 to 1000 and try to find the number of prime consecutive numbers that can occur in that sequence.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 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, 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, 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, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997.

Here if we notice the above given prime numbers from 1 to 1000 numbers. The ones digit of the prime numbers are all odd numbers except the 2, also the 2 and 3 are the consecutive numbers and also prime numbers.

The 2 and 3 are the only prime consecutive numbers as all the other higher values are  with odd values, however these may satisfy the condition of prime consecutive odd numbers. the consecutive number in the list of prime numbers do not occur.