The Strange Mind Of Eureka Blip Puzzle

The Puzzle:

The Strange Mind Of Eureka Blip
Welcome to the strange mind of Eureka Blip.

He does not always think the same way as we do, but he does always have his own logical set of rules. One of his favourite tricks is to say the opposite of what he really means. Recently I had a conversation with him, which went like this:

"Good morning, Eureka, how are you?"
"Go away. I feel absolutely dreadful."
"What are you thinking about today?"
"I am not thinking of any number at all."
"Is your number less than 50?"
"No. It is greater than 50, and it is a prime number."
"Is it less than 26?"
"Yes, and it is an even number."
"And it's not a square number?"
"Thank you, Eureka. Goodbye."
"Please. Hello."

What was Eureka Blip thinking of?
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