Block #504,182

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/21/2014, 3:09:01 PM · Difficulty 10.8080 · 6,308,109 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f83f3ecd1319a714585168a89fec2e14ee5ac369d04a21d5dd23c8488ce716f

View on Chainz ↗

Height

#504,182

Difficulty

10.808006

Transactions

Size

1.00 KB

Version

Bits

0aced97e

Nonce

18,479,088

Timestamp

4/21/2014, 3:09:01 PM

Confirmations

6,308,109

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

2ac14dd99dda03b35569effc0d73efdb90d3561eb3c790c405bb283aae89ad15

Transactions (2)

Coinbase659a923d11b06c…8ad9e122e33af6

1 in → 1 out8.5600 XPM116 B

AbwWkWZt…kawDhufa

80d0ce41148094…7bd46af72578e6

5 in → 2 out3.3296 XPM818 B

AGtwxD3Y…sGyeJm16 AQ236kx1…SA7ixpmc

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.

3.762 × 10⁹⁸(99-digit number)

37624421285268583462…25639938742070929899

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

3.762 × 10⁹⁸(99-digit number)

37624421285268583462…25639938742070929899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.762 × 10⁹⁸(99-digit number)

37624421285268583462…25639938742070929901

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

7.524 × 10⁹⁸(99-digit number)

75248842570537166925…51279877484141859799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.524 × 10⁹⁸(99-digit number)

75248842570537166925…51279877484141859801

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

1.504 × 10⁹⁹(100-digit number)

15049768514107433385…02559754968283719599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.504 × 10⁹⁹(100-digit number)

15049768514107433385…02559754968283719601

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

3.009 × 10⁹⁹(100-digit number)

30099537028214866770…05119509936567439199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.009 × 10⁹⁹(100-digit number)

30099537028214866770…05119509936567439201

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

6.019 × 10⁹⁹(100-digit number)

60199074056429733540…10239019873134878399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.019 × 10⁹⁹(100-digit number)

60199074056429733540…10239019873134878401

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 #504,182

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