Block #405,382

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/15/2014, 12:56:19 PM · Difficulty 10.4305 · 6,403,685 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aba795355b1f5657f4b2fa06ff86e1ad7feb7a6bed2e6da6943eabd15e825c95

View on Chainz ↗

Height

#405,382

Difficulty

10.430547

Transactions

Size

778 B

Version

Bits

0a6e385a

Nonce

453,817

Timestamp

2/15/2014, 12:56:19 PM

Confirmations

6,403,685

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2f366fff1ed74f44e63d4b1db490d9dc2c86ccc9426b2c90746eaa9a7ac5dc48

Transactions (2)

Coinbase3334817e63b25a…8a31cb5db83050

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

97781645a1085b…3640707f4438b4

2 in → 9 out10.6458 XPM578 B

AJ7bwxHw…vy276KPV ALdGgGD9…dPTNDfjE AYxooQUP…AxKVt9CF AMyfScyn…AbNHprpR ASY5xqVU…DNRfWDXj

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.

4.707 × 10⁹³(94-digit number)

47073725325526805821…08439005197340514359

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

4.707 × 10⁹³(94-digit number)

47073725325526805821…08439005197340514359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.707 × 10⁹³(94-digit number)

47073725325526805821…08439005197340514361

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

9.414 × 10⁹³(94-digit number)

94147450651053611642…16878010394681028719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.414 × 10⁹³(94-digit number)

94147450651053611642…16878010394681028721

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

1.882 × 10⁹⁴(95-digit number)

18829490130210722328…33756020789362057439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.882 × 10⁹⁴(95-digit number)

18829490130210722328…33756020789362057441

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

3.765 × 10⁹⁴(95-digit number)

37658980260421444656…67512041578724114879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.765 × 10⁹⁴(95-digit number)

37658980260421444656…67512041578724114881

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

7.531 × 10⁹⁴(95-digit number)

75317960520842889313…35024083157448229759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.531 × 10⁹⁴(95-digit number)

75317960520842889313…35024083157448229761

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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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

Cross-reference on Chainz Explorer

Block #405,382

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