Aptitude - Numbers - Discussion

Table of Prime Number up to 1000.

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

If any given number is prime or not, how can u find out? here is one way to solve for that one.

Step 1:

Find the square root for given number. if it is not a perfect square take nearest number of that on.

Ex: 91 is given. 8 is nearest square root (81) [91<x^2]

Step 2:

Write all prime numbers below that square root number.

2 3 5 7

Step 3:

If the given number(91) is not divisible with any one of the above numbers(2 3 5 7) then that number is prime number otherwise it's not.

We can use the elimination method here.

The question says we need a number that is completely divisible by (2^32 + 1). So, a number that satisfies this condition will be larger than the given number.

Option A and B are obviously smaller.

Option C and D are the choices.

On a closer analysis we find that even option c is smaller than the actual number.

So we are left with option D as our final answer. You need to use your wit rather than calculation to solve a problem.

For 3 numbers calculation:

Let us find whether 149 is prime or not.
[square root of 149= 12.20 < 13] prime numbers below 13 are 2,3,5,7,11.
149 is not exactly divisible by 2, because it don't has even number at the end.
149 is not exactly divisible by 3, because the sum of numbers 1+4+9= 14 is not divisible by 3.
149 is not exactly divisible by 5, because it don't has 0 or 5 at the end.
149 is not exactly divisible by 7,11.
So, 149 is a prime number.

Hiii friends .......just apply this formula to find the not prime no or prime no...
n*n>=p
1)here P is the given no
2)find the squares which is > or = to the given no P
3)find the prime nos < or = n
4)check weather the given P no is divisible by prime nos which is < or =n
5)if divisible ....it mean it have more than two factors so given P is not a prime no.
6)if not divisible it mean the given no P is prime no

The Question is "which is not a prime number".

In a very simple way how do we check whether a number is prime or not, .

The number should be divisible by one & the number it self right!.
Now see their options, that are, .

31. - is a prime number which can only be divided 1 & the number itself.
61. - same here.
71. - here too.
91. - is divisible by 1, 7, 91.

So, among other options, 91 is not a prime number.

First you memorize these below numbers,

2, 3, 5, 7.

1--1379.

2--39.

3--17.

4--137.

5--39.

6--17.

7--139.

8--39.

9--7.

These are the shortcuts for prime number. Lets see, 1--1379 means 11 is prime, 13 is prime, 17 is prime, 19 is prime. Likewise 2--39 means 23 is prime, 29 is prime. This is the easy way to memorize the prime number. Its very easy (just you have to memorize the above given no).

6k + 1 or 6k - 1 is a simplified form. Any prime number always satisfies this condition,where k can be 1,2,3...9.

But plz Note: Every prime no can be written in the form of 6k+1,6K-1 But every no which can be written in the form of 6k+1,6k-1 are not necessarily prime.

Here 91 can be written as 6k + 1 = 6(15) + 1 where k = 15,
But it is not prime as it is divisible by 13,7.

2, 3, 5, 7.

1--1379.

2--39.

3--17.

4--137.

5--39.

6--17.

7--139.

8--39.

9--7.

These are the shortcuts for the prime number.
Lets see, 1--1379 means 11 is prime, 13 is prime, 17 is prime, 19 is prime.
Likewise 2--39 means 23 is prime, 29 is prime. This is the easy way to memorize the prime number. Its very easy (just you have to memorize the above given no).

This is the easiest way to check prime number.

Ex that 31, So put the nearest square of this number 25<31>36, so square of 31 is something 5. Something, then find the number below 5 prime number i.e. 2 and 3, now check 31 is divisible by this number or not if this is divisible then it is not the prime number, if this is not divisible then it is a prime number.