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Block #397,076

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/9/2014, 8:11:52 PM · Difficulty 10.4155 · 6,444,515 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa0a5d7aa4efc4e2e62db7b9b43a0fbca3c7ad4fef09f673db039b640b7d8f77

View on Chainz ↗

Height

#397,076

Difficulty

10.415547

Transactions

Size

903 B

Version

Bits

0a6a614a

Nonce

4,388

Timestamp

2/9/2014, 8:11:52 PM

Confirmations

6,444,515

Merkle Root

874094b1d0f125201d9cc94cae3fdce0f8ff0b1ee9db556412673ab0994077a2

Transactions (1)

Coinbase874094b1d0f125…673ab0994077a2

1 in → 22 out9.2000 XPM811 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 Aac9Hjdg…P4ktypc3 ALqxX1WA…hsKjbnXn Af76ewER…EzGhbQ6S

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.

2.193 × 10⁹⁹(100-digit number)

21938596047986795523…19009155739521381280

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

2.193 × 10⁹⁹(100-digit number)

21938596047986795523…19009155739521381279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.193 × 10⁹⁹(100-digit number)

21938596047986795523…19009155739521381281

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

4.387 × 10⁹⁹(100-digit number)

43877192095973591047…38018311479042762559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.387 × 10⁹⁹(100-digit number)

43877192095973591047…38018311479042762561

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

8.775 × 10⁹⁹(100-digit number)

87754384191947182095…76036622958085525119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.775 × 10⁹⁹(100-digit number)

87754384191947182095…76036622958085525121

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

1.755 × 10¹⁰⁰(101-digit number)

17550876838389436419…52073245916171050239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.755 × 10¹⁰⁰(101-digit number)

17550876838389436419…52073245916171050241

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

3.510 × 10¹⁰⁰(101-digit number)

35101753676778872838…04146491832342100479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.510 × 10¹⁰⁰(101-digit number)

35101753676778872838…04146491832342100481

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 397076

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 aa0a5d7aa4efc4e2e62db7b9b43a0fbca3c7ad4fef09f673db039b640b7d8f77

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 #397,076 on Chainz ↗

Block #397,076

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