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Block #431,904

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 12:48:05 PM · Difficulty 10.3429 · 6,394,672 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

71a1189b2976a95986a64ee6b9ec76530b3d244e70d4878dddf4c1fe1eb95f9f

View on Chainz ↗

Height

#431,904

Difficulty

10.342879

Transactions

Size

424 B

Version

Bits

0a57c6e3

Nonce

84,278

Timestamp

3/6/2014, 12:48:05 PM

Confirmations

6,394,672

Merkle Root

1e04c871eb5e870ba6c8f303420c5f9bc38fc15931f4b108653375d0dd972be0

Transactions (2)

Coinbasec923a707906a25…5b5ec77a1d9744

1 in → 1 out9.3400 XPM110 B

AeKNrjNj…1NEq95Ta

47a479543f35bf…43ee04cfd5e1b5

1 in → 2 out1781.9682 XPM225 B

APvMG9X2…VbTpQLrt AJwSBgMT…bcbgCVtZ

Prime Chain Origin

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.

4.228 × 10⁹²(93-digit number)

42286118530600960747…97362716536642385920

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

4.228 × 10⁹²(93-digit number)

42286118530600960747…97362716536642385919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.228 × 10⁹²(93-digit number)

42286118530600960747…97362716536642385921

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

8.457 × 10⁹²(93-digit number)

84572237061201921495…94725433073284771839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.457 × 10⁹²(93-digit number)

84572237061201921495…94725433073284771841

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

1.691 × 10⁹³(94-digit number)

16914447412240384299…89450866146569543679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.691 × 10⁹³(94-digit number)

16914447412240384299…89450866146569543681

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

3.382 × 10⁹³(94-digit number)

33828894824480768598…78901732293139087359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.382 × 10⁹³(94-digit number)

33828894824480768598…78901732293139087361

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

6.765 × 10⁹³(94-digit number)

67657789648961537196…57803464586278174719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.765 × 10⁹³(94-digit number)

67657789648961537196…57803464586278174721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 431904

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 71a1189b2976a95986a64ee6b9ec76530b3d244e70d4878dddf4c1fe1eb95f9f

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 #431,904 on Chainz ↗

Block #431,904

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