Home/Chain Registry/Block #331,673

Block #331,673

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2013, 12:58:01 PM · Difficulty 10.1683 · 6,462,684 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5ad64c034eb5f310c0a34b6c9cfca7aa9039a600d6912a65649deb1d9b2c0a5

View on Chainz ↗

Height

#331,673

Difficulty

10.168293

Transactions

Size

204 B

Version

Bits

0a2b153f

Nonce

174,109

Timestamp

12/27/2013, 12:58:01 PM

Confirmations

6,462,684

Merkle Root

d0f7d370321d0a96fc3d40220a530546a3285839b0d496f966f7063973c017fe

Transactions (1)

Coinbased0f7d370321d0a…f7063973c017fe

1 in → 1 out9.6600 XPM116 B

AbwWkWZt…kawDhufa

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.

4.578 × 10⁹⁰(91-digit number)

45780793820235560655…31559732764653537700

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

4.578 × 10⁹⁰(91-digit number)

45780793820235560655…31559732764653537699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.578 × 10⁹⁰(91-digit number)

45780793820235560655…31559732764653537701

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

9.156 × 10⁹⁰(91-digit number)

91561587640471121310…63119465529307075399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.156 × 10⁹⁰(91-digit number)

91561587640471121310…63119465529307075401

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

1.831 × 10⁹¹(92-digit number)

18312317528094224262…26238931058614150799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.831 × 10⁹¹(92-digit number)

18312317528094224262…26238931058614150801

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

3.662 × 10⁹¹(92-digit number)

36624635056188448524…52477862117228301599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.662 × 10⁹¹(92-digit number)

36624635056188448524…52477862117228301601

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

7.324 × 10⁹¹(92-digit number)

73249270112376897048…04955724234456603199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.324 × 10⁹¹(92-digit number)

73249270112376897048…04955724234456603201

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 331673

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 b5ad64c034eb5f310c0a34b6c9cfca7aa9039a600d6912a65649deb1d9b2c0a5

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 #331,673 on Chainz ↗