Sunday, January 4, 2009

[b]6k+ ......or........- 1



There are infinite prime numbers .......but there should be some pattern existing between the sequence of prime numbers ..........in general all d prime numbers greater than 3 follow the equation 6k + or - 1 ......fine[:)] 
But jus think........ does all numbers equal to 6k+1 or 6k-1(k ranging from 1 to infinite)are prime numbers [:-?]......when u consider any one ............such as 6k-1 or 6k+1 they will miss the pattern dat is all prime numbers are equal to 6k+1 or 6k-1................ but not viceversa so d pattern fails here.
So dis is not enough to recognise the correct pattern we have to generalize the given equation........much more.........now lets consider 6k+1........ when k=4 the value is 25 and the pattern fails ........again when k=8 the value is 49 which are not prime numbers .........jus observe der is one thing common here i.e...when  k=4n(n=1to infinite) ........at dis values only the pattern but for other cases it works gud...............so k should not be a multiple of 4 .......den d pattern will be right..............but when k=4*4(n=4)value is 97 wich is again a prime number................huuuuuu...................again the pattern fails..........when k=4*8(n=4*2)value is 193 which is  a prime..............so from above results we can see dat when n is a multiple of 4 the assumption is going wrong(k!=4n)......................so we can say the pattern for 6k+1 will be right only when k!=4n and n!=multiple of  4......now check it...............by consider the values of k wid the above constarints...............ur pattern will be right................[:-D].........

Now lets check out for 6k-1........now let k=6 den the value iz 35 which is not a prime when k=11 den the value is 65 again it is a prime ....from above results we can see dat when k=5n+1(n ranging from 1 to infinity)the pattern goes wrong...............so to get the right pattern k!=5n+1  simple................

So to get a right a pattern here we have to generalize the equations much more as given above 
....................as dis is a simple one we can get the pattern by further generealizing the equations......but imagine the universal equations like[b]E=mc*c[/b]................
Eg:-A stationary body has no velocity den according to einsteins model E=mc*c which is applicable everywhere in d universe...........but a stationary body has no velocity den it should not have any energy but it has energy in it [b]HOW??????????????[/b][:->]
 

5 comments:

sirish aditya said...

mawa! bagundi raa but its very complicated...i understood it 'coz i was with you when you wrote this but not everyone can understand it...try making it simpler...but anyhow, a good effort...[:D]

Sravani said...

whoa!!dat's nice..but like aditya said ..it's way too complicated dude...maybe u shud explain it to us lyke u explain stuff during da exams!!!-:)...wud be much better..watsay???

Sai Kishore Bandaru said...

Yeah its a bit complicated but when u try dem on d paper in a order u will get it.........but maths is always complex[;)]

The GenZBharatha Team said...

hey a body is said to be stationary with reference to what?? thats should be mentioned right?..suppose consider a body is said to be at rest with respect to u but its moving with respect to the earth....so probably the einstein's equation holds good that way!!

Sai Kishore Bandaru said...

evrybody on earth when it is rest it is taken wid respect to earth so ur answer is correct but relative velocity w.r.t earth is zero.......and if u consider universe to be infinity every point can be taken as focus so den w.r.t wat point ur velocity is taken .....