Prime Time: an original card game by David Parlett

I've always wanted to invent a game called Intellectual Snap, in which the winning of cards depended on thought or calculation rather than just visual reaction speed. Here's a basic idea that should suit anyone who likes mental arithmetic and is partial to prime numbers.

Cards

Three players each receive 18 cards from a 54-card pack including two Jokers. (For two players, see below.)

Play

Hold your cards face down in a pile as for ordinary Snap. At each turn you simultaneously turn the top card of your pile and slap it face up on the table. As soon as you can, you then call out a prime number that can be made by combining all three of the numbers displayed on those three cards. For this purpose -

Each ace counts 1
numerals 2 to 10 count at face value
each face card counts 5
a Joker counts exactly the same as the higher of the other two visible cards.

Combining them means putting them into an equation yielding a prime. For example, from 4-6-8 you can make 3 (= [6 x 4] ÷ 8, or 6 ÷ [8 ÷ 4]).

Note: Any division used must be integral - that is, leave no remainder. For example, from 2-7-9 you can't claim 31 = 7 x 9 ÷ 2, as the result is actually 31½.

Reminder: You may need reminding that, by convention, 1 is not a prime number. Thus the lowest is 2, followed by 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97...

If you call first you must demonstrate that the calculation is correct and the result is indeed prime. If so, you win those three cards and add them face down to the bottom of your hand. If not, you may not call again on the same three cards, but the others may. If another player calls a higher valid prime before anyone has started to the next round, the higher one wins. If two or more players call the same number simultaneously you each bury the card you played somewhere in your pile of hand cards and turn the next instead. The same applies if no one can make a prime, though this should never happen. (At least, I can't find any three-card combination that fails. Can you?) Keep playing till somebody has won all 54 cards.

House rules

High primes: Agree whether or not you are allowed primes greater than 97. Not recommended, unless you all know your three-figure primes by heart, or are willing to use a crib.
Juxtaposition: Agree whether or not you can juxtapose numerals - by, for example, putting a 7 and an 8 together and calling them 78 (or 87). Not recommended, except for children.
Face cards: You may wish to ascribe values other than 5 to face cards, such as Jack 11, Queen 12, King 13. The problem with 5 is that you will often have to make a prime from three face cards, to which the only answer I can see is 5 (= 5 + 5 - 5, or 5 x (5 ÷ 5, or even 5^[5 ÷ 5].) Perhaps better is to count face cards at their suit value rather than their face-less value. For this purpose I favour spades 1, hearts 2, clubs 3, diamonds 4.
Powers and roots: Agree whether or not you may use powers and roots. For example, from 2-3-6 you can claim 67 = 2⁶ + 3. (Recommended.)
Other functions: Agree any other functions you may wish to recognise. For example, from 5-6-8 are you allowed 97 = 6 + [triangular (5 + 8)]?

FOR TWO PLAYERS

Start: Deal 18 cards each and 18 face up to the table to form a stockpile. Play as above, with the top card of the stockpile counting as the third card at each turn.
Continuation: When all the cards have been won, prepare for the next round as follows. You each contribute your top nine cards to form an 18-card stockpile and continue as before. Keep playing and redealing until one of you cannot contribute nine cards to a new stockpile, or has no card left in hand after doing so. That player loses.
Footnote: If you like equation games, see also Brain Drain, Equator, and One Up