Prime factorization can be extended from just the positive integers to all the positive rational numbers if we allow negative exponents on the primes. For example, the prime factorization of 25/24 is 2^-3 * 3^-1 * 5^2.
So, what would negative exponent prime effects do in Strategems? Since these effects divide the energy cost of the stone, they have to be bad for you - and considering how strong dividing a card's energy cost by something like 53 is, some of the later effects need to be really detrimental to justify being able to reduce a stone with a cost in the upper four-digit range into something playable with 100 energy!
1/2. Burn a tile in this row or column. The fire lasts for three turns instead of two, i.e. it ends on your opponent's next next turn.
1/3. Your opponent gets to cycle a card
1/5. Freeze one of your stones in this row or column
1/7. Vulnerable: Cannot be placed adjacent to any fire, and if any of your stones adjacent to this one are frozen then this stone isn't valid for territory extending
1/11. Any empty tiles orthogonally adjacent to this stone are "blocked" from your color, meaning you cannot place stones on them but your opponent can.
1/13. All of the cards currently in your opponent's hand cost 13 less.
1/17. Any empty tiles diagonally adjacent to this stone are blocked from your color
1/19. Destroy adjacent stones of your color.
1/23. Any empty tiles exactly two orthogonal tiles in one direction away from this stone are blocked from your color
1/29. Exhaust this card.
1/31. Add a stone of the opponent's color in this row or column
1/37. Adds a 1/37 to your opponent's hand. Exhaust.
1/41. Invert all adjacent stones that are yours
1/43. The next card you play costs double energy
1/47. Cannot be played adjacent to an opponent's stone
1/53. Lose your next turn after this current turn (this stacks, so if you play two of these effects you lose your next two turns)
1/59. Adds one "stoneless card" to your deck (a stoneless card cannot be played, it's just deadweight in your hand)
1/61. Discard your highest card. If this is your highest card when you play it, it discards itself instead of letting you add it to the board.
1/67. Discard 2 cards. You cannot play this stone if you have less than two other cards in your hand when you play it.
1/71. When you play this card, you may only choose one of its prime factors to use the effect of (if it has any), not counting the 1/71 itself. (Both primes like 2 and reciprocals of primes like 1/2 count as one prime factor, so if you had 30/77 then you could choose 2, 3, 5, 1/7, or 1/11. The energy cost is not altered by this choice, only the effect).
1/73. Your opponent gets the effect of the next stone you play instead of you
1/79. Surround with stones in the opponent's color
1/83. Surround diagonal spots with stones in the opponent's color
1/89. Give a card to your opponent
1/97. May be played in any empty space. Your opponent gets to choose where this stone goes when you play it.