Number Relationships ( Trivia # 24 )

Here are some beautiful Number Relationships.
Notice the consecutive exponents :



Now, taken one place further, we get :

Good Primes ( Trivia # 21 )

Erdös and Strauss defined a good prime as a prime number whose square is greater than the product of any two primes at the same number of positions before and after it in the sequence of primes.

p (n)^2 > p (n − i) * p (n + i)

for all values of i from 1 to n − 1.

The infinite sequence of good primes starts :
5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149 ........

Truncatable Primes ( Trivia # 19 )

In number theory, a left-truncatable prime is a prime number which, in a given base, contains no 0, and if the leading ("left") digit is successively removed, then all resulting numbers are prime.
For example 9137, since 9137, 137, 37 and 7 are all prime.

There are exactly 4260 decimal left-truncatable primes:

2, 3, 5, 7, 13, 17, 23, 37, 43,
47, 53, 67, 73, 83, 97, 113, 137, 167, 173,
197, 223, 283, 313, 317, 337, 347, 353, 367, 373,
383, 397, 443, 467, 523, 547, 613, 617, 643, 647,
653, 673, 683, 743, 773, 797, 823, 853, 883, 937,
947, 953, 967, 983, 997, 1223, 1283, 1367 ...

The largest left-truncatable prime is the 24-digit 357686312646216567629137.

A right-truncatable prime is a prime which remains prime when the last ("right") digit is successively removed.
For example 7393, since 7393, 739, 73, 7 are all prime.

There are 83 right-truncatable primes. The complete list:

2, 3, 5, 7, 23,
29, 31, 37, 53, 59,
71, 73, 79, 233, 239,
293, 311, 313, 317, 373,
379, 593, 599, 719, 733,
739, 797, 2333, 2339, 2393,
2399, 2939, 3119, 3137, 3733,
3739, 3793, 3797, 5939, 7193,
7331, 7333, 7393, 23333, 23339,
23399, 23993, 29399, 31193, 31379,
37337, 37339, 37397, 59393, 59399,
71933, 73331, 73939, 233993, 239933,
293999, 373379, 373393, 593933, 593993,
719333, 739391, 739393, 739397, 739399,
2339933, 2399333, 2939999, 3733799, 5939333,
7393913, 7393931, 7393933, 23399339,
29399999, 37337999, 59393339, 73939133

The prime 73939133 is the largest right-truncatable prime that repeatedly produces primes when digits are deleted from the right.
The numbers 73939133, 7393913, 739391, 73939, 7393, 739, 73, and 7 are all prime.

Siamese primes ( Trivia # 18 )

Named by Beauregard and Suryanarayan, they are prime pairs of the form n^2 − 2 and n^2 + 2. The sequence of pairs starts :

7-11
79-83
223-227
439-443
1087-1091
13687-13691
.. . . .

Riesel number ( Trivia # 17 )

A Riesel number is an integer k such that k.2^n − 1 is composite for any integer value of n.
Riesel found k = 509203 in 1956.
The Riesel conjecture is that this is the smallest Riesel number.

Kaprekar Constant ( Trivia # 14 )

Step 1: Take any 4 digits number,such that at least 2 of its digits are different.

Step 2: Write the digits in ascending order.

E.g If I take 7526, the ascending order form is taking the smallest digit first, to the biggest diggit last. In this case, its 2567.

Step 3: Write the digits in descending order.

E.g If I take 7526, the descending order form is taking the biggest digit first, to the smallest diggit last. In this case, its 7652.

Step 4: Find the difference between the two resulting numbers.

In the example in steps 2 and 3, we are doing the following operation:-
7652-2567

Step 5: Repeat Steps 2,3 and 4 for the resulting difference we get in step 4.

In less than 8 steps you sall get 6174. Work it out for yourself.

eg: Take the number: 4884

Ascending order: 4488 Descending order; 8844 Difference: 4356

Ascending order: 3456 Descending order; 6543 Difference: 3087

Ascending order: 0378 Descending order; 8730 Difference: 8352

Ascending order: 2358 Descending order; 8532 Difference: 6174

Can anyone say what would be the case for 3 digited numbers?????

Why is Negative * Negative = Positive ??? ( Trivia # 13 )

One way to think of numbers is in terms of money. Let's say you and I are playing poker. To make life convenient, we use chips instead of real money. A green chip is worth Rs.5. A red chip means that you owe Rs.5. So if you lose Rs.5, you can represent that by giving up a green chip, or (if you're out) by picking up a red chip. Of course, you are always allowed to pick up a green chip and a red chip at the same time, because that doesn't change your total sum. (At the end, presumably, we'll cash in all our chips and see who gains or loses what money.)

I hope you see the mathematical analogy I'm drawing here: A green chip represents +Rs.5, and a red chip represents -Rs.5. Make sense? If so, here comes multiplication in terms of chips.

If you gain three green chips, what happens? Intuitively, you know that you gain Rs.15. Mathematically, we take the +Rs.5 that one chip is worth, and multiply it by +3, to indicate that you are gaining three chips. 3 x Rs.5 = Rs.15; positive times positive is positive.

If you gain three red chips, what happens? If you think about it, I think you'll agree that you just lost Rs.15. Mathematically, this looks the same as the previous example, except that the +Rs.5 that represents a green chip, is replaced by -Rs.5 to represent a red chip. 3 x -Rs.5 = -Rs.15; positive times negative is negative.

Now, what if you lose three green chips? Once again, you have lost Rs.15. We represent this "loss" mathematically by changing the 3 into a -3, so our equation is: -3 x Rs.5 = -Rs.15. Negative times positive is negative.

And finally, what if you lose three red chips? Hooray! This is happy news, it means you have actually gained money. Mathematically, this is -3 (since you lost) times -Rs.5 (since they were red chips). -3 x -Rs.5 = +Rs.15. Negative times negative is positive.

Finally, for people who like algebraic sorts of proofs, consider this. A and B are both positive numbers.

A + (-A) = 0
(A)(B) + (-A)(B) = 0

Since the term on the left is positive, the term on the right must be negative. (I'm assuming here that if two non-zero numbers add up to zero, then one of them is negative and one is positive—I think that is too obvious to require a proof.) This proves that negative times positive is negative. Now:

A + (-A) = 0
(A)(-B) + (-A)(-B) = 0

Since the term on the left is negative (as we just proved!), the term on the right must be positive.

Number Patterns #2 ( Trivia # 12 )

Hey guys check this out :

1 * 8 + 1 = 9
12 * 8 + 2 = 98
123 * 8 + 3 = 987
1234 * 8 + 4 = 9876
12345 * 8 + 5 = 98765
123456 * 8 + 6 = 987654
1234567 * 8 + 7 = 9876543
12345678 * 8 + 8 = 98765432
123456789 * 8 + 9 = 987654321


1 * 9 + 2 = 11
12 * 9 + 3 = 111
123 * 9 + 4 = 1111
1234 * 9 + 5 = 11111
12345 * 9 + 6 = 111111
123456 * 9 + 7 = 1111111
1234567 * 9 + 8 = 11111111
12345678 * 9 + 9 = 111111111
12346789 * 9 + 10 = 1111111111


9 * 9 + 7 = 88
98 * 9 + 6 = 888
987 * 9 + 5 = 8888
9876 * 9 + 4 = 88888
98765 * 9 + 3 = 888888
987654 * 9 + 2 = 8888888
9876543 * 9 + 1 = 88888888
98765432 * 9 + 0 = 888888888

Sexy Primes ( Trivia # 11 )

Sexy primes are such that n and n + 6 are both prime. “Sexy” comes from the Latin for “six,” which as all schoolboys know, is sex.

The sexy pairs under 200 are:
5-11 , 11-17 , 13-19 ,
17-23 , 23-29 , 31-37 ,
37-43 , 47-53 , 53-59 ,
61-67 , 67-73 , 73-79 ,
83-89 , 97-103 , 103-109 ,
107-113 , 131-137 , 151-157 ,
157-163 , 167-173 , 173-179 , and 191-197.

LOVE { 0 } ( Trivia # 7 )

The term ‘ love ’, meaning 0 , in tennis is derived from the French ‘ l’oeuf ’, meaning ‘ the egg ’ – an egg looking not unlike a 0. The same thinking gave rise to the use of ‘ duck ’ in cricket for a batsman’s score of 0. Scratch is the golfing term for 0, as in ‘ scratch out ’, meaning to erase. A ‘scratch golfer’ plays off a 0 handicap. Nil is a term that is rarely used outside the field of sport (one exception being the medical phrase ‘nil by mouth’, meaning ‘not to be swallowed’). Nil is a simple abbreviation of ‘ nihil ’, the Latin word for nothing.

Bateman’s conjecture ( Trivia # 6 )

Is this the only sum of this kind, using prime numbers? No one knows. If composite numbers are allowed, there is at least one other solution:

Number Pattern # 1 (Trivia # 3)

There are times when the charm of mathematics lies in the surprising nature of its number system. There are not many words needed to demonstrate this charm. It is obvious from the patterns attained. So i hope u'll appreciate this charm of number pattern ....

1 * 1 = 1
11 * 11 = 121
111 * 111 = 12321
1111 * 1111 = 1234321
11111 * 11111 = 123454321
111111 * 111111 = 12345654321
1111111 * 1111111 = 1234567654321
11111111 * 11111111 = 123456787654321
111111111 * 111111111 = 12345678987654321