The queried name and this guide
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A constrained four-by-four board
Prime Divisor Sum Mines has 16 cells labelled 1 to 16, read across each row. Choose 3, 4 or 5 hazards before starting. For each hazard label, count its positive divisors; only complete layouts whose divisor counts add to a prime number are allowed. A prime is an integer above 1 with exactly two positive divisors. Each allowed layout is equally likely. There are 170 layouts with 3 hazards, 635 with 4 and 1,473 with 5. The labels define this constraint; they are not adjacent-hazard clues.
Probability after a safe reveal
A round deducts the selected stake once. Its initial gross quoted value is 97% of that stake, but collection is disabled before the first safe reveal. Safe observations remove incompatible layouts. For an unopened cell, P is the proportion of remaining layouts in which it is safe. A successful reveal changes the current gross value to current value ÷ P. At P = 1 the value stays unchanged. A hazard ends the round with zero gross return. Gross return includes the stake component; it is not net profit.
Actual controls and stopping rules
Stakes are 10, 20, 50 or 100 play coins; defaults are stake 20 and 3 hazards. During a round, stake, hazard selection and balance restoration are locked, and another round cannot start. Sound and eligible cell choices remain available. The random-choice button selects an eligible cell; it does not guarantee safety. Collection becomes available after one safe reveal. Known hazards and choices with prospective gross value above 1,000 times the captured stake are disabled; equality is allowed. After a safe reveal the game banks automatically when no eligible uncertain cell remains, even if known-safe cells are unopened.
Whole coins and fractional carry
At settlement, the game adds the raw gross return to the saved fractional carry, then credits the whole-number part rounded down. The remaining fraction is saved for later settlements. For example, 24.984848… plus carry 0.2 credits 25 coins and leaves about 0.184848 carry. The fraction is added before rounding. Zero-return rounds preserve the old carry and do not refund the stake. The displayed rounded quote does not replace the underlying calculation.
Local balance and manual restoration
The wallet starts at 1,000 play coins only when no valid saved balance is available. A saved balance, including zero, is reused. While no round is active and the balance is below 10, manual restoration sets it to exactly 1,000; it does not add 1,000 or clear fractional carry. The coins have no cash value and no deposit or withdrawal flow is provided. Restoration is a demo control, not recovery of a lost stake.
Frequently asked questions
Are the printed labels hazard clues?
They identify cells for the divisor-count constraint, not neighboring-hazard counts. Safe probabilities come from the remaining compatible layouts.
When does automatic collection happen?
After a safe reveal, when no eligible uncertain cell remains. Known-safe unopened cells may still remain. Manual collection needs at least one safe reveal.
When is fractional carry added?
It is added to raw gross return before rounding down to whole coins. The remaining fraction is saved; a zero return keeps the old carry.
