Firstly, all the Siddhas are great. They have achieved the status of Siddha by doing things that ordinary people could not do.
What is so special about the number 18 ?
Though the exact reason is unknown. But the number 18 has a special place in the Hinduism. There are 18 puranas; 18 steps to Sabarimala; 18 days of Mahabharat war like this 18 has found a special place in Hindu way of life. This might have lead to coming up with a number that is not too low, for identfying the most common of Siddhas.
Why are there 18 great Siddhas?
Though the exact reason for secluding 18 Siddhas among the hundreds of other Siddhas is unknown, one can assume that these 18 Siddhas must have achieved something more than other Siddhas. One of the theory is that only these 18 Siddhas attained the Asthama Siddhis, where as others achinved some, but not all. Some other theory suggests that, the 18 find a place because of their popularity among people. Regardless of the reason, there is a list of 18 and this list varies from author to author.
The "Great 18"
Lord Siva is the Siddhas's Siddha. He is the paramaguru for all the Siddhas, directly or indirectly. His first and primary disciple is Nandi, the bull. So, Nandi is considered as the first Siddha. Nandi's disciples are Pathanjali and Agastya. Since, Nandi has attained a special place with the Lord as his transport, he is excluded from the list.
Where were they born and attained Samadhi?
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Who are the great 18 Siddhas?