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][:->]
