Block #451,147

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/19/2014, 5:50:25 PM · Difficulty 10.3822 · 6,365,433 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b332762a0375af3a022021db06955c923318eb30a09c8ea4605fe2a85413a403

View on Chainz ↗

Height

#451,147

Difficulty

10.382170

Transactions

Size

391 B

Version

Bits

0a61d5e5

Nonce

124,035,728

Timestamp

3/19/2014, 5:50:25 PM

Confirmations

6,365,433

Mined by

⛏️ P2SHARbkCSmHBjwFi6NqcHUUhzo2j9GPH3qT3u

Merkle Root

db37601bb7eba8b6efe02f2d5e0a90677bd2da20eabea1700a9aa4e57f7340d8

Transactions (2)

Coinbase767fdd9ac6e9d3…f906b00e85dc56

1 in → 1 out9.2700 XPM109 B

ARbkCSmH…GPH3qT3u

04f06773045235…225e775b17b7a0

1 in → 2 out9.3100 XPM192 B

Ac7dbpaZ…XL2MrsxW ALe73byb…gZoPcGoS

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.

5.048 × 10⁹⁴(95-digit number)

50486887332065770034…57204379263729706319

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

5.048 × 10⁹⁴(95-digit number)

50486887332065770034…57204379263729706319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.048 × 10⁹⁴(95-digit number)

50486887332065770034…57204379263729706321

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

1.009 × 10⁹⁵(96-digit number)

10097377466413154006…14408758527459412639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.009 × 10⁹⁵(96-digit number)

10097377466413154006…14408758527459412641

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

2.019 × 10⁹⁵(96-digit number)

20194754932826308013…28817517054918825279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.019 × 10⁹⁵(96-digit number)

20194754932826308013…28817517054918825281

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

4.038 × 10⁹⁵(96-digit number)

40389509865652616027…57635034109837650559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.038 × 10⁹⁵(96-digit number)

40389509865652616027…57635034109837650561

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

8.077 × 10⁹⁵(96-digit number)

80779019731305232055…15270068219675301119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.077 × 10⁹⁵(96-digit number)

80779019731305232055…15270068219675301121

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 #451,147

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