Do you Know?

1. 31              is a prime number.
331                is a prime number.
3331              is a prime number.    
33331            is a prime number.
333331          is a prime number.
3333331        is a prime number.
33333331      is a prime number.
333333331    is NOT a prime number. Because 333333331 =17*19607843.
MATHEMATICS ALWAYS NEEDS PROOF.

2. If you break the number 3025 into two parts 30 and 25, the square of 30 + 25 is equal to 3025. Square of   55   = 3025.  In   the same way 2025= (20+25)2.

3. When Square of an odd number is divided by 8, then the remainder is always 1. Exception odd number 1.

4. The sum of two consecutive triangular numbers is a square number. 

5. The product of four consecutive integers is divisible by 24.

6. The product of five consecutive integers is divisible by 120.

7. 153 is an interesting number. The number can be expressed as the sum of cubes of its digits. 153= 1³+5³+3³.

8. Product of two prime numbers is a semi prime number. 4,6. 9,10,14,…are semi primes.

9. Every odd number greater than 7 is the sum of three prime numbers.

10. 1, 2, 3 the three numbers have the same answer when added together and multiplied together.

11. It’s very interesting to know that, there are some numbers whose sum of all the digits of that cubic value is that number.
Examples: 17³ =4913 and 4+9+1+3 = 17
8³ =512 and 5+1+2=8.

12.   3, 4, 5 is a Pythagorean triplet.
33, 44, 55 is also is a Pythagorean triplet.
333,444,555 is also a Pythagorean triplet.
3333, 4444, 5555 is also a Pythagorean triplet.  

13. Sum of 10 Fibonacci numbers is equal to the 11 times the seventh Fibonacci number.
Example: Addition of below 10 Fibonacci number is 143
1, 1, 2, 3, 5, 8, 13, 21, 34, 55
And the 7th Fibonacci number which is 13 multiplied by 11 is also 143.

14. The product of three consecutive integers is always a multiple of 6.

15. nth derivate of  xn is equal to n!

16. If a, b, c, d are four integers then( a2+b2 )( c2+d2)=(ac-b d)2 +(ad +b c)2 or (ac+ bd)2 +(ad-bc)2. This relation is called  Brahmagupta –Fibonacci Identity.

Multiplication Trick for any 3 digit number with 143

Here   I am showing you a mental trick of multiplying any three digit number by 143.


    Step 1:- Take any three digit number.  For example:  587

   Step 2:- Picture the three digit number twice in your mind as 587587.

   Step 3:- divide the above six digit number by seven as 587587/7 = 83,941

83,941 is the answer of 587*143. With little more practice you can do this very easily.

Another example:Let us multiply 253 by 143.

1.  Write the number(253 ) two times 253253
2.  Divide by 7: 253253/7 = 36179
3. Thus 253 multiplied by 143=36179

Verify it. Take more examples and practice it.