Block #465,717

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2014, 4:09:24 PM · Difficulty 10.4232 · 6,346,630 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2cfe9ced19a1818e12fa992d4542aa9430032ef2bfa114ece4c0b24f6b69700c

View on Chainz ↗

Height

#465,717

Difficulty

10.423169

Transactions

Size

891 B

Version

Bits

0a6c54c6

Nonce

247,631

Timestamp

3/29/2014, 4:09:24 PM

Confirmations

6,346,630

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

5801ece965f22091ca36b104741682d77bc6830d6381266134cdf5f1ce231d9f

Transactions (2)

Coinbase9c0b38cb5f2372…a2cee7cd75eda0

1 in → 1 out9.2000 XPM110 B

AeKNrjNj…1NEq95Ta

fc030c8edcf8b7…ac2010ad130aa5

3 in → 10 out28.3900 XPM691 B

Af5JcoF1…bCtmmgeZ AYKiwoLg…2bSJSJ59 AWpvCBBf…yE35vgWj AeKNrjNj…1NEq95Ta Ac6MfyWU…Jo4dNcQk

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.

1.165 × 10⁹⁵(96-digit number)

11656400301779090202…73561093072372010199

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

1.165 × 10⁹⁵(96-digit number)

11656400301779090202…73561093072372010199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.165 × 10⁹⁵(96-digit number)

11656400301779090202…73561093072372010201

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

2.331 × 10⁹⁵(96-digit number)

23312800603558180405…47122186144744020399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.331 × 10⁹⁵(96-digit number)

23312800603558180405…47122186144744020401

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

4.662 × 10⁹⁵(96-digit number)

46625601207116360811…94244372289488040799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.662 × 10⁹⁵(96-digit number)

46625601207116360811…94244372289488040801

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

9.325 × 10⁹⁵(96-digit number)

93251202414232721622…88488744578976081599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.325 × 10⁹⁵(96-digit number)

93251202414232721622…88488744578976081601

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

1.865 × 10⁹⁶(97-digit number)

18650240482846544324…76977489157952163199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.865 × 10⁹⁶(97-digit number)

18650240482846544324…76977489157952163201

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 #465,717

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