Block #1,187,183

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/8/2015, 8:21:03 PM · Difficulty 10.8793 · 5,628,898 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

97a397a2e00cbc819367136badeee9304d8de56495839d66ad9616516cd80d94

View on Chainz ↗

Height

#1,187,183

Difficulty

10.879275

Transactions

Size

2.44 KB

Version

Bits

0ae1182e

Nonce

1,981,301,346

Timestamp

8/8/2015, 8:21:03 PM

Confirmations

5,628,898

Mined by

⛏️ P2SHAQxpCqWGQTUo3DTxGuJH9fpn17rPJsEadp

Merkle Root

1f12d3a6921c374188d0161b637fbacef374b5a0f8bebc525184acebfd6fb1ab

Transactions (2)

Coinbased6a5f3a9da74eb…5809af1c766533

1 in → 1 out8.5000 XPM109 B

AQxpCqWG…rPJsEadp

27cd50b061f0dc…b4d4aa86cf3a95

15 in → 2 out259.5907 XPM2.24 KB

AJVeRHXf…C2yREH1f ATjpzesr…irTm9Rve

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.

3.607 × 10⁹⁷(98-digit number)

36079612620192100927…44988277012897955839

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

3.607 × 10⁹⁷(98-digit number)

36079612620192100927…44988277012897955839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.607 × 10⁹⁷(98-digit number)

36079612620192100927…44988277012897955841

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

7.215 × 10⁹⁷(98-digit number)

72159225240384201855…89976554025795911679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.215 × 10⁹⁷(98-digit number)

72159225240384201855…89976554025795911681

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

1.443 × 10⁹⁸(99-digit number)

14431845048076840371…79953108051591823359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.443 × 10⁹⁸(99-digit number)

14431845048076840371…79953108051591823361

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

2.886 × 10⁹⁸(99-digit number)

28863690096153680742…59906216103183646719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.886 × 10⁹⁸(99-digit number)

28863690096153680742…59906216103183646721

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

5.772 × 10⁹⁸(99-digit number)

57727380192307361484…19812432206367293439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.772 × 10⁹⁸(99-digit number)

57727380192307361484…19812432206367293441

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 #1,187,183

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