How Prime Exponent Range Claim Works

Twelve steps reveal the terminal score

Twelve independent fair binary steps reveal three blocks of four bits. Each complete block is a binary number from 0 to 15; add one to obtain three integers from 1 to 16. The complete round is chosen before the reveal begins.

For every prime appearing in those integers, compare its exponents in the three prime factorizations. An absent prime has exponent zero. Subtract the smallest exponent from the largest and add those differences to get the reward score. The minimum score is zero.

If all twelve revealed bits are zero, the three integers are 1, 1 and 1, giving a terminal score of zero. In Linear, the quote starts at 0.97, is approximately 0.897702 after step 1 and 0.606501 after step 6, then reaches zero at step 12 if the round has not already settled.

For a scoring example, the integers 8, 4 and 1 have exponents 3, 2 and 0 for the prime 2. The exponent range is 3, so the score is 3 and the Linear, Square and Cube weights are 3, 9 and 27.

How the gross quote is calculated

Linear uses the terminal reward score as its weight. Square uses the score squared, and Cube uses the score cubed. Each curve has its own initial average terminal weight across all 4,096 equally likely complete outcomes.

At each reveal, average the terminal weights of the outcomes still consistent with the revealed bits. The current gross quote is 0.97 times that conditional average divided by the curve's initial average. It starts at 0.97 and can rise, fall or reach zero. It is a gross multiplier, rather than an amount of profit.

Settings and manual collection

Choose a stake of 10, 20, 50 or 100 play coins, a Linear, Square or Cube curve, and an automatic collection setting before pressing Start the claim. The defaults are 20 coins, Linear and Auto off. One stake is deducted when the round starts.

The stake, curve and automatic threshold selectors, balance restoration and a second round are locked until settlement. The main action remains available as Collect current quote, and sound remains available. Selected settings remain after settlement; reloading restores 20, Linear and Auto off.

During an active round, Collect current quote asks to settle at the current gross multiplier. Before paying, the game processes every reveal step due since the round began, with a step due every 450 milliseconds. A click therefore cannot collect a stale displayed quote while bypassing elapsed events.

A zero quote settles with no return before collection at that event. An automatic crossing at an earlier step settles before a later zero can be processed. If the round remains active after the elapsed steps are processed, manual collection pays the current quote.

Automatic first crossing and step 12

Automatic collection can be off or set to 1.25, 1.75 or 2.50. It settles at the first positive quote that reaches or exceeds the chosen threshold. The whole quote is paid, including any overshoot; the payout is not capped at the preset.

Zero settles first at the same event. An earlier automatic crossing settles before a later zero event. If no earlier settlement occurs, step 12 collects a surviving positive quote even when it is below the automatic threshold. A zero terminal quote gives no return.

Exact expectation and saved samples

The exact expected gross return is 97% for the checked stopping policies: collection at step 6, terminal settlement at step 12, and first crossing at 1.25, 1.75 or 2.50. Each was checked with Linear, Square and Cube, giving fifteen curve-and-policy combinations.

Saved simulations used one million rounds for each combination. Their measured returns ranged from about 96.902% to 97.100%. These are sample observations, separate from the exact expectation. A 97% expected return is not a win probability, a guaranteed collection or a session target.

For Linear, the saved step-6 sample measured about 96.991%; its terminal sample measured 96.980%. For Square, the 1.75 first-crossing sample measured 97.066%; for Cube, the terminal sample measured 97.100%. Each used one million rounds. None promises the same return in a player's session.

Settlement, wallet and reloads

Multiply the settled gross quote by the captured stake to obtain the raw gross return. Add the saved fractional carry, credit the whole-number part, and save the remaining fraction. For example, 12.4 coins of raw return plus 0.8 carry credits 13 coins and saves 0.2.

A zero-return round leaves the carry unchanged. Carry persists through settlement, restoration and reload. Gross return is the total credited from a round, rather than profit added on top of the stake already deducted.

A new wallet starts with 1,000 play coins. The balance and fractional payout carry are saved in browser local storage, including a settled zero balance. These coins have no cash value and cannot be bought, withdrawn or exchanged for money.

When no round is active and the balance is strictly below 10, Restore balance sets it to exactly 1,000. It replaces the old balance rather than adding 1,000 coins and keeps the fractional carry. Restoration is manual.

Reloading during an unfinished round ends it. The stake already deducted stays deducted, with no refund, payout, continuation or resumption. The saved wallet and carry remain, while stake, curve and automatic selection return to 20, Linear and Auto off.

Collect or let the round settle before reloading if you want its return credited. Local saved state is not an online account or a guarantee of recovery after browser data are removed.

Frequently asked questions