Block #188,812

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/1/2013, 10:24:02 AM · Difficulty 9.8714 · 6,638,101 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c9831b1d55c8c4e26a4e2c1f5dca8867e233756ab02b2bdc57dd1447aa3106c3

View on Chainz ↗

Height

#188,812

Difficulty

9.871352

Transactions

Size

866 B

Version

Bits

09df10ef

Nonce

93,509

Timestamp

10/1/2013, 10:24:02 AM

Confirmations

6,638,101

Mined by

⛏️ P2SHAWPh3V4bLAUTpZrnMtPLg7AJBJSbWA19so

Merkle Root

e43b3c95b01e577bf4c9bb0ab5a236408a240efed19f87f26939dadf764ef739

Transactions (2)

Coinbase4eaa466c5cf276…c2236f740e33d6

1 in → 1 out10.2600 XPM109 B

AWPh3V4b…SbWA19so

5e385bd6983e9a…a564052039268b

4 in → 2 out2.0300 XPM668 B

ARhqsz72…N3HPDhpM AUF3joRB…QSfPsP5Y

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.

2.762 × 10⁹²(93-digit number)

27628621843065594032…39184747037347253599

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

2.762 × 10⁹²(93-digit number)

27628621843065594032…39184747037347253599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.762 × 10⁹²(93-digit number)

27628621843065594032…39184747037347253601

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

5.525 × 10⁹²(93-digit number)

55257243686131188064…78369494074694507199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.525 × 10⁹²(93-digit number)

55257243686131188064…78369494074694507201

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

1.105 × 10⁹³(94-digit number)

11051448737226237612…56738988149389014399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.105 × 10⁹³(94-digit number)

11051448737226237612…56738988149389014401

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

2.210 × 10⁹³(94-digit number)

22102897474452475225…13477976298778028799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.210 × 10⁹³(94-digit number)

22102897474452475225…13477976298778028801

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

4.420 × 10⁹³(94-digit number)

44205794948904950451…26955952597556057599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.420 × 10⁹³(94-digit number)

44205794948904950451…26955952597556057601

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 #188,812

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