diff --git a/contracts/Proofs.sol b/contracts/Proofs.sol
index a442789..bca3cfe 100644
--- a/contracts/Proofs.sol
+++ b/contracts/Proofs.sol
@@ -36,7 +36,10 @@ abstract contract Proofs is Periods {
 
   function _getPointer(SlotId id, Period period) internal view returns (uint8) {
     uint256 blockNumber = block.number % 256;
-    uint256 periodNumber = Period.unwrap(period) % 256;
+    // To ensure the pointer does not remain in downtime for many consecutive
+    // periods, for each period increase, move the pointer 67 blocks. We've
+    // chosen a prime number to ensure that we don't get cycles.
+    uint256 periodNumber = (Period.unwrap(period) * 67) % 256;
     uint256 idOffset = uint256(SlotId.unwrap(id)) % 256;
     uint256 pointer = (blockNumber + periodNumber + idOffset) % 256;
     return uint8(pointer);