Block #467,337

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/30/2014, 5:15:27 PM · Difficulty 10.4364 · 6,342,850 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5ec9752626e8c86291ecc735f01218a728600bfea0269cb57f8ab076c45b520a

View on Chainz ↗

Height

#467,337

Difficulty

10.436439

Transactions

Size

427 B

Version

Bits

0a6fba79

Nonce

93,573

Timestamp

3/30/2014, 5:15:27 PM

Confirmations

6,342,850

Mined by

⛏️ P2SHAdNTU9GgjevXsvCYo11ARtbiMoqdcbRVLk

Merkle Root

09bc67f1958ebe0afde1f17f00a228416c79e9dedec6b1444842f58a4d6d6e06

Transactions (2)

Coinbase4f0b3001a60823…24d3adee7a4cbd

1 in → 1 out9.1800 XPM110 B

AdNTU9Gg…qdcbRVLk

3b8748eee4d083…d1a848deee6052

1 in → 2 out1.0250 XPM226 B

ALurxLnB…pWguH7uF ATH2UEva…DVMtoM4W

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.

6.526 × 10⁹⁶(97-digit number)

65265791232684986901…55713834818407148799

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

6.526 × 10⁹⁶(97-digit number)

65265791232684986901…55713834818407148799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.526 × 10⁹⁶(97-digit number)

65265791232684986901…55713834818407148801

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

1.305 × 10⁹⁷(98-digit number)

13053158246536997380…11427669636814297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.305 × 10⁹⁷(98-digit number)

13053158246536997380…11427669636814297601

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

2.610 × 10⁹⁷(98-digit number)

26106316493073994760…22855339273628595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.610 × 10⁹⁷(98-digit number)

26106316493073994760…22855339273628595201

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

5.221 × 10⁹⁷(98-digit number)

52212632986147989521…45710678547257190399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.221 × 10⁹⁷(98-digit number)

52212632986147989521…45710678547257190401

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

1.044 × 10⁹⁸(99-digit number)

10442526597229597904…91421357094514380799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.044 × 10⁹⁸(99-digit number)

10442526597229597904…91421357094514380801

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 #467,337

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