This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.512 × 10⁹³(94-digit number)

15120767974008353198…08338267278425896960

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.512 × 10⁹³(94-digit number)

15120767974008353198…08338267278425896959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.512 × 10⁹³(94-digit number)

15120767974008353198…08338267278425896961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.024 × 10⁹³(94-digit number)

30241535948016706397…16676534556851793919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.024 × 10⁹³(94-digit number)

30241535948016706397…16676534556851793921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

6.048 × 10⁹³(94-digit number)

60483071896033412795…33353069113703587839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.048 × 10⁹³(94-digit number)

60483071896033412795…33353069113703587841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.209 × 10⁹⁴(95-digit number)

12096614379206682559…66706138227407175679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.209 × 10⁹⁴(95-digit number)

12096614379206682559…66706138227407175681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.419 × 10⁹⁴(95-digit number)

24193228758413365118…33412276454814351359

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 9

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 254690

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 4af1847df022d0fbb2de3913e783fa08a21c1945007f9998a7e11a4b0a7bc7ea

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #254,690 on Chainz ↗

Block #254,690

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