Home/Chain Registry/Block #336,371

Block #336,371

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/30/2013, 10:09:13 PM · Difficulty 10.1417 · 6,457,973 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b7e1559637fc9fcc8bd342d74f60014f11dfa1be1d3477f7f21ec9ac997063d

View on Chainz ↗

Height

#336,371

Difficulty

10.141747

Transactions

Size

201 B

Version

Bits

0a244986

Nonce

160,809

Timestamp

12/30/2013, 10:09:13 PM

Confirmations

6,457,973

Merkle Root

c34bc44f6a2db93e53162c4cf070d021ec82086f59ea0a609bd9b2cad32416f8

Transactions (1)

Coinbasec34bc44f6a2db9…d9b2cad32416f8

1 in → 1 out9.7100 XPM110 B

AeKNrjNj…1NEq95Ta

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.

7.662 × 10⁹⁵(96-digit number)

76621179723980421016…72684756648497937120

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

7.662 × 10⁹⁵(96-digit number)

76621179723980421016…72684756648497937119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.662 × 10⁹⁵(96-digit number)

76621179723980421016…72684756648497937121

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

1.532 × 10⁹⁶(97-digit number)

15324235944796084203…45369513296995874239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.532 × 10⁹⁶(97-digit number)

15324235944796084203…45369513296995874241

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

3.064 × 10⁹⁶(97-digit number)

30648471889592168406…90739026593991748479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.064 × 10⁹⁶(97-digit number)

30648471889592168406…90739026593991748481

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

6.129 × 10⁹⁶(97-digit number)

61296943779184336813…81478053187983496959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.129 × 10⁹⁶(97-digit number)

61296943779184336813…81478053187983496961

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

1.225 × 10⁹⁷(98-digit number)

12259388755836867362…62956106375966993919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.225 × 10⁹⁷(98-digit number)

12259388755836867362…62956106375966993921

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 336371

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 2b7e1559637fc9fcc8bd342d74f60014f11dfa1be1d3477f7f21ec9ac997063d

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 #336,371 on Chainz ↗