2, 3, 5, 9, 17, _ What is the next number in the sequence?

What is the next number in this series?

4,12,84,3612....

A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

John is found dead in a bare field. Nobody killed John,
John did not commit suicide.

Inspector Jacob found a bag just a few meters away from John which could save his life. What was in the bag?

Find The Next Number in the series:

12 13 15 17 111 113 117 119 123 ?

what's the probability of getting a king or a queen from a pack of 52 cards?

Which is the smallest number that you can write using all the vowels exactly once?

John was writing his first book. After saving the document, he locked his laptop with a password and mentioned some phrases for the hint box.

A friend of his tried opening his laptop but found out that it was password protected. Following is the hint that appeared.
1 mobile 3 books 2 roars 1 night 4 balls 2 lighters 1 ghost 1 hat 3 watches.

Can you help him in cracking the password?