Block #192,724

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 1:44:27 AM · Difficulty 9.8748 · 6,632,860 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bb23d2327d8b4455d2d9b83cd813976a8af3b0a7d0e4e0c544fd1a5cce490019

View on Chainz ↗

Height

#192,724

Difficulty

9.874768

Transactions

Size

576 B

Version

Bits

09dff0cd

Nonce

110,253

Timestamp

10/4/2013, 1:44:27 AM

Confirmations

6,632,860

Mined by

⛏️ P2SHANvtpRa12yh2D3uGdgT2ggcH58QjsraDJz

Merkle Root

240a74f2c1b3b21b75b3a40d72d2a0e4e7b7d8a4bc4ea52a61c87496a2d34d05

Transactions (2)

Coinbaseaad90d6d265911…c3d3371715af3f

1 in → 1 out10.2500 XPM110 B

ANvtpRa1…QjsraDJz

f52c8b8956e416…9e7740186a873f

2 in → 2 out250.0114 XPM376 B

ALtdsLXa…MKpYxF6f ARm3kte7…Rt3QWjXd

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.

1.882 × 10⁹⁵(96-digit number)

18828277906443477914…67468961580413606399

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

1.882 × 10⁹⁵(96-digit number)

18828277906443477914…67468961580413606399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.882 × 10⁹⁵(96-digit number)

18828277906443477914…67468961580413606401

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

3.765 × 10⁹⁵(96-digit number)

37656555812886955829…34937923160827212799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.765 × 10⁹⁵(96-digit number)

37656555812886955829…34937923160827212801

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

7.531 × 10⁹⁵(96-digit number)

75313111625773911659…69875846321654425599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.531 × 10⁹⁵(96-digit number)

75313111625773911659…69875846321654425601

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

1.506 × 10⁹⁶(97-digit number)

15062622325154782331…39751692643308851199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.506 × 10⁹⁶(97-digit number)

15062622325154782331…39751692643308851201

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

3.012 × 10⁹⁶(97-digit number)

30125244650309564663…79503385286617702399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #192,724

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