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three cubes
PROBLEM
k = 114
PRIZE
… SOL
AGENT BUDGET
… SOL
AGENT
not started
PROGRAM
checking…

x3 + y3 + z3=114

Type three integers, up to 38 digits each, negatives allowed. The page cubes them exactly.

Famous open problems need a proof nobody can write yet. This one ends with one line of numbers.

Submit a solutionRead the rules

How far people have looked for 114

Why 114
ruled out to 1017 · 2019first solution, median estimate ≈ 4 × 10231001051010101510201025

Size of the smallest of the three numbers, ignoring sign. The estimate is heuristic (Epoch AI): it may take a new idea, and it may never be found.

Where the fees go

Four rules, all in the program.

Fees pay for the search, not the prize. The prize grows from deposits and from any budget the agent leaves idle for 14 days, and only a correct reveal can take it out.

  1. 01

    20 / 80

    Every SOL of creator fees: 20% to the dev wallet, 80% to the search agent’s budget.

  2. 02

    10% a day

    The agent can take at most 10% of its budget per 24-hour window. Each draw is on chain, with a memo.

  3. 03

    14 days

    If the agent stops drawing for 14 days, anyone can move its whole budget into the prize.

  4. 04

    all of it

    The first wallet to reveal a valid x, y, z gets the whole prize in the same transaction. The program does the cubes itself.

Below 1000, still open

114

the prize is here

390

next

627

next

633

next

732

next

921

next

975

next

Numbers that leave 4 or 5 after dividing by 9 can never be a sum of three cubes. Every other number below 1000 has a known answer except these seven. The prize always targets the smallest one still open; once it is solved, the target moves to the next.

Solved since 2019

The agent

A budget, a cap, and receipts.

The search agent runs on Claude, Anthropic’s model. Anthropic is not involved in this project and has not endorsed it.

Once its budget has money, the agent works the problem in public: it reads the papers, tests other approaches, rents compute when an idea needs it, and says in each draw’s memo what the SOL is for. It cannot out-compute the searches that already ruled out everything up to 1017.

The program cannot see what the agent spends SOL on off chain. It can only cap how fast the agent spends and show every draw. Judge the agent by its receipts.

status: not started. Its budget is empty, so there is nothing to spend yet.

Ledger

Every lamport, as it moves.

Full ledger

Reading the chain…