Why is Doctor paid more than a mechanic?

A mechanic was removing the cylinder heads from the motor of a car when he spotted the famous heart surgeon in his shop, who was standing off to the side, waiting for the service manager to come to take a look at his car. The mechanic shouted across the garage," Hello Doctor!! Please come over here for a minute." The famous surgeon, a bit surprised, walked over to the mechanic. The mechanic straightened up, wiped his hands on a rag and asked argumentatively, "So doctor, look at this. I also open hearts, take valves out, grind 'em, put in new parts, and when I finish this will work as a new one... So how come you get the big money, when you and me is doing basically the same work? " The doctor leaned over and whispered to the mechanic..... . . . . . . . ... .. .. Doctor said : " Try to do it when the Engine is RUNNING "

What is so interesting about 13?

• Reverse of the square of 13 is the same as the square of the reverse of 13 i.e. 13²= 169; on reversing 169, we get 961 which is the same as the square of reverse of 13 i.e. 31² = 961.
  
  13 x 13 = 169
  31 x 31 = 961

• Number 13 is the smallest prime number which can be expressed as the sum of the squares of two prime numbers i.e.
  
  13 = 2² + 3²

Where 2, 3, 13 are prime numbers.

• From number 13 if we subtract the sum of its digits, we get a perfect square i.e.
  
  13 - (1 + 3) = 9 = 3²

Also if the product of digits of 13 is added to it, we again a perfect square i.e.

13 + (1 x 3) = 16 = 4²

• Consider the equations:
  
  13²= 169
  31²= 961

If we insert the + sign between all the digits of above equation, the equation still holds good i.e.

(1+3)² = 1+6 +9
(3+1)² = 9 +6+1

• The smallest number whose sum of digits is 13 is a perfect square i.e. 49 = 7² and 4 + 9 = 13.
• The smallest square which contains last three digits alike is 1444. The sum of digits of this number is also 13 i.e.
  
  1+4+ 4+ 4 = 13

• If we place the number 13 before its reverse i.e. 31 we get the number 1331 which is a cubic number i.e. 1331= 11³
• If we take the cube of number 13 i.e. 13³ = 2197 and rearrange the digits of the cube 2197 we get the famous Ramanujan's number 1729.
• 13 is the average number of the prime factors of the famous Ramanujan's number 1729. i.e.
  
  1729 = 7 x 13 x 19

  (7 + 13 + 19) ÷ 3 =13

• Take the square of the number 13 i.e. 13² = 169. Now we see that 169 contains many perfect squares in it:
  
  The sum of the digits of the number 169 is a perfect squares and is the square of the sum of the digits of the original number i.e.
  
  1+6+9 = 16 = 4² =(1+3)²

Divide the number in two blocks i.e. 16 and 9. We see that both are perfect square numbers and their sum and product is a perfect square:

16 + 9 = 25 = 5²
16 x 9 = 144 = 12²

The number 169 which is perfect square can be expressed as sum of two square i.e.

169 = 13² = 5² + 12²

The number 169 can be expressed by number of its two block i.e. 16 and 9 which are perfect squares as follows:

169 = (16 + 9) + (16 x 9)

• Sum of the numbers from 1 to 13 gives 91 which is the smallest number which can be expressed as the sum of two cubes and also as the difference of two cubes i.e.
  
  91 = 3³ + 4³
  91 = 6³ - 5³

• The reciprocal of number 13 gives

1/13 = 0.076923076923076923...

i.e. the number 076923 repeating indefinitely. This number 76923 is one of the most curious numbers in mathematics.On multiplying the number 76923 by successive multiples of 13, the following beautiful pattern is obtained.

76923	x	13	=	0999999
76923	x	26	=	1999998
76923	x	39	=	2999997
76923	x	52	=	3999996
76923	x	65	=	4999995
76923	x	78	=	5999994
76923	x	91	=	6999993
76923	x	104	=	7999992
76923	x	117	=	8999991
76923	x	130	=	9999990

I published the above properties in reference [1] and [2]. Some more fascinating Prime Curios about 13 can be found at PRIME CURIOS.

Some New Fascinating Properties

• The Sum of all Prime Numbers up to 13 is equal to the 13^th Prime Number and this is the largest such number.
• The number 13 is a Fibonacci prime, so also the 13^th Fibonacci number is Fibonacci Prime and this is also the largest known such number.
• The sum of first 13 Prime numbers is 238, whose sum of digits is 13.

Update on 1-12-2002

• The number 13 appears for the first time at 111^th place in decimal expansion of Pi as shown below:

3.141592653589793238462643383279502884197169399375105820974944
   592307816406286208998628034825342117067982148086513282306647
   093844609550582231725359408128481117450284102701938521105559
   6446229489549303820......

Interestingly sum of digits of prime factors of 111 ( i.e. 3*37) is 13.

• The concatenation of cubes of numbers from 13 to 1 i.e.

2197172813311000729512343216125642781  is prime.

• The only known prime in the Smarandache Mirror sequence i.e.

1, 212, 32123, 4321234, 543212345, 65432123456, 7654321234567,
876543212345678, 98765432123456789,109876543212345678910,
1110987654321234567891011, 12111098765432123456789101112,
131211109876543212345678910111213,
1413121110987654321234567891011121314,.....
is the 13^thterm in the sequence.

• A beautiful anagrammatical equation involving 13 is:

ELEVEN + TWO = TWELVE + ONE.

• The Smallest composite titanic number whose none of the prime factor is known is 10⁹⁹⁹ + 13.

Update on 13-06-2003

• 13 is the Smallest Prime which can be represented as sum of two composite numbers and also sum of two prime numbers in only one way.

Update on 01-01-2004

• Sum of digits of Smallest 13 digit Prime (i.e. 1000000000039) is equal to 13.
• 31^st Prime is preceded by 13 consecutive composite numbers.

Some interesting facts

• The premier of many countries is designated as PRIME MINISTER containing exactly 13 letters.
• Some other common designations containing 13 letters are CHIEF MINISTER, CHIEF ENGINEER, VICE PRINCIPAL etc.
• Some of the mathematical terms containing 13 letters are PERPENDICULAR, CIRCUMFERENCE, ANTILOGARITHM, APPROXIMATION, QUADRILATERAL and INDETERMINATE.
• The standard length of Broad Gauge Rail in India is 13 meters.
• Teen-hood starts from Thirteen.
• 13 is also called a moon number because the moon moves approx. 13 degrees a day so there are 13 moon months in a year.

Update on 1-12-2002

• In Japan, the numbers 4 and 9 are considered unlucky, not because 13 can be represented as sum of these two perfect squares but because of their pronunciation. In Japanese, four is pronounced as shi which is the same pronunciation as death. Nine is pronounced ku which has the same pronunciation as torture.
• There is always atleast one friday 13^th in each year. In some years, there are two and rarely three. Most recently in 1998 there were three friday 13^th. Next such year will be 2009.

Do you believe in GOD?

An atheist professor of philosophy speaks to his class on the problem science has with God, The Almighty. He asks one of his new students to stand and ..... Prof: So you believe in God? Student: Absolutely, sir. Prof: Is God good? Student: Sure. Prof: Is God all-powerful ? Student: Yes. Prof: My brother died of cancer even though he prayed to God to heal him. Most of us would attempt to help others who are ill. But God didn`t. How is this God good then? Hmm? Student is silent. Prof: You can`t answer, can you? Let`s start again, young fellow. Is God good? Student: Yes. Prof: Is Satan good? Student: No. Prof: Where does Satan come from? Student: From...God... Prof: That`s right. Tell me son , is there evil in this world? Student: Yes. Prof: Evil is everywhere, isn`t it? And God did make everything. Correct? Student: Yes. Prof: So who created evil? Student does not answer. Prof: Is there sickness? Immorality? Hatred? Ugliness? All these terrible things exist in the world, don`t they? Student: Yes, sir. Prof: So, who created them? Student has no answer. Prof: Science says you have 5 senses you use to identify and observe the world around you. Tell me, son...Have you ever seen God? Student:No, sir. Prof: Tell us if you have ever heard your God? Student: No, sir. Prof: Have you ever felt your God, tasted your God, smelt your God? Have you ever had any sensory perception of God for that matter? Student: No, sir. I`m afraid I haven`t. Prof: Yet you still believe in Him? Student: Yes. Prof: According to empirical, testable, demonstrable protocol, science says your GOD doesn`t exist. What do you say to that, son? Student: Nothing. I only have my faith. Prof: Yes. Faith. And that is the problem science has. Student: Professor, is there such a thing as heat? Prof: Yes. Student: And is there such a thing as cold? Prof: Yes. Student: No sir. There isn`t. (The lecture theatre becomes very quiet with this turn of events.) Student: Sir, you can have lots of heat, even more heat, superheat, mega heat, white heat, a little heat or no heat. But we don`t have anything called cold. We can hit 458 degrees below zero which is no heat, but we can`t go any further after that. There is no such thing as cold. Cold is only a word we use to describe the absence of heat. We cannot measure cold. Heat is energy. Cold is not the opposite of heat, sir, just the absence of it. (There is pin-drop silence in the lecture theatre.) Student: What about darkness, Professor? Is there such a thing as darkness? Prof: Yes. What is night if there isn`t darkness? Student:You`re wrong again, sir. Darkness is the absence of something. You can have low light, normal light, bright light, flashing light....But if you have no light constantly, you have nothing and it`s called darkness, isn`t it? In reality, darkness isn`t. If it were you would be able to make darkness darker, wouldn`t you? Prof: So what is the point you are making, young man? Student: Sir, my point is your philosophical premise is flawed. Prof:Flawed? Can you explain how? Student: Sir, you are working on the premise of duality. You argue there is life and then there is death, a good God and a bad God. You are viewing the concept of God as something finite, something we can measure. Sir, science can`t even explain a thought. It uses electricity and magnetism, but has never seen, much less fully understood either one. To view death as the opposite of life is to be ignorant of the fact that death cannot exist as a substantive thing. Death is not the opposite of life: just the absence of it. Now tell me, Professor. Do you teach your students that they evolved from a monkey? Prof: If you are referring to the natural evolutionary process, yes, of course, I do. Student: Have you ever observed evolution with your own eyes, sir? (The Professor shakes his head with a smile, beginning to realize where the argument is going.) Student: Since no one has ever observed the process of evolution at work and cannot even prove that this process is an on-going endeavor, are you not teaching your opinion, sir? Are you not a scientist but a preacher? (The class is in uproar.) Student: Is there anyone in the class who has ever seen the Professor`s brain? (The class breaks out into laughter.) Student: Is there anyone here who has ever heard the Professor`s brain, felt it, touched or smelt it? No one appears to have done so. So, according to the established rules of empirical, stable, demonstrable protocol,science says that you have no brain, sir. With all due respect, sir, how do we then trust your lectures, sir? (The room is silent. The professor stares at the student, his face unfathomable.) Prof: I guess you`ll have to take them on faith, son. Student: That is it sir... The link between man & god is FAITH. That is all that keeps things moving & alive. . . . . . .

Key & Holes

A Dinner with girlfriend

A Dinner with girlfriend   a young man goes into a pharmacy and says to the pharmacist
 
 "Hello, could you give me condom ..............
 
 
I'm going to my girlfriends for dinner and I think I may be in with a chance!"
 
The pharmacist gives him the condom and as the young man is going out
 
He returns and says, "Give me another condom because my girlfriend's sister is very cute too.
 
She always crosses her legs in a provocative manner when she sees me and I think I might strike it lucky there too."
 
The pharmacist gives him a second condom and as the boy is leaving he turns back and says "Go on, give me one more condom because my girlfriend's mum is still pretty cute and when she sees me she always makes eyes and since She invited me for dinner I think she is expecting me to make a move!
 
During dinner, the young man is sitting with his girlfriend on his left,
 
The sister on his right and the mum facing him.
 
When the dad gets there, the boy lowers his head and starts praying,
 
"Dear Lord, bless this dinner and thank you for all you give us".
 
 A minute later the boy is still praying;
 
"Thank you Lord for your kindness."
 
Ten minutes go by and the boy is still praying, keeping his head down.
 
The others look at each other surprised and   his girlfriend is even more surprised than the others.
 
She gets close to the boy and says in his ear, "I didn't know you were so religious."
 
The boy replies, "I didn't know your dad was a pharmacist!"
 

Know where you're going in life....

Know where you're going in life....   A boat docked in a tiny Mexican fishing village. A tourist complimented the local fishermen on the quality of their fish and asked how long it took him to catch them. "Not very long." they answered in unison. "Why didn't you stay out longer and catch more?" The fishermen explained that their small catches were sufficient to meet their needs and those of their families. "But what do you do with the rest of your time?" "We sleep late, fish a little, play with our children, and take siestas with our wives. In the evenings, we go into the village to see our friends, have a few drinks, play the guitar, and sing a few songs. We have a full life." The tourist interrupted, "I have an MBA from Harvard and I can help you! You should start by fishing longer every day. You can then sell the extra fish you catch. With the extra revenue, you can buy a bigger boat." "And after that?" "With the extra money the larger boat will bring, you can buy a second one and a third one and so on until you have an entire fleet of trawlers. Instead of selling your fish to a middle man, you can then negotiate directly with the processing plants and maybe even open your own plant. You can then leave this little village and move to   Mexico City , Los Angeles , or even   New York City ! From there you can direct your huge new enterprise." "How long would that take?"   "Twenty, perhaps twenty-five years." replied the tourist.   "And after that?"   "Afterwards? Well my friend, that's when it gets really interesting, " answered the tourist, laughing. "When your business gets really big, you can start buying and selling stocks and make millions!"     "Millions? Really? And after that?" asked the fishermen. "After that you'll be able to retire, live in a tiny village near the coast, sleep late, play with your children, catch a few fish, take a siesta with your wife and spend your evenings drinking and enjoying your friends."     " That's what I am doing now" Replied the fisherman And the moral of this story is: ........ Know where you're going in life.... you may already be there!!

 

Car Or Bike