Teaser 2834

Degrees of freedom

I bought an odd thermometer from an old curiosity shop. On its linear scale the freezing point and boiling point of water were higher than they are on the centigrade scale. In fact the freezing point was a prime number and, higher up the scale, the boiling point was a perfect square. There was only one number on the scale where it actually agreed with the corresponding centigrade temperature. That number was the negative of an odd prime (and not the same prime as the one mentioned earlier).

On this new scale, what are the freezing and boiling points of water?

Send your solution to: The Sunday Times Teaser 2834, PO Box 29, Colchester, Essex CO2 8GZ or email puzzle.entries@sunday-times.co.uk. The first two correct solutions opened after next Saturday win £20.