Block #176,189

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/22/2013, 7:20:23 PM · Difficulty 9.8647 · 6,623,092 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4ddee9f499e9ab4ed44e6b21315c0a98c1742ed9caaa37f953c06582ffc45a6f

View on Chainz ↗

Height

#176,189

Difficulty

9.864655

Transactions

Size

1.22 KB

Version

Bits

09dd5a10

Nonce

67,214

Timestamp

9/22/2013, 7:20:23 PM

Confirmations

6,623,092

Mined by

⛏️ P2SHAX8gCoZJxCXoAoKCf8Pr4oVqsqSxgjTDoW

Merkle Root

655954a015b79352ec10dfca960936f44192d74c06808a97f66b6bfc8535b72c

Transactions (3)

Coinbasee2fe11432f4094…7764a390fb19d9

1 in → 1 out10.2800 XPM109 B

AX8gCoZJ…SxgjTDoW

fa66a95a98d90f…c5918a6a6655ee

5 in → 2 out51.3300 XPM821 B

AVCFzPjC…ezBsALLc ATx7J3QS…CyXUcpwB

af5fe7745bb571…f0f43e4293b75b

1 in → 2 out5.1126 XPM227 B

AHLqQjYK…4CDrWv66 ATU52EgT…yJxD6Bue

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.

4.501 × 10⁹⁶(97-digit number)

45013931919962128665…99454848437978560639

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

4.501 × 10⁹⁶(97-digit number)

45013931919962128665…99454848437978560639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.501 × 10⁹⁶(97-digit number)

45013931919962128665…99454848437978560641

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

9.002 × 10⁹⁶(97-digit number)

90027863839924257331…98909696875957121279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.002 × 10⁹⁶(97-digit number)

90027863839924257331…98909696875957121281

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

1.800 × 10⁹⁷(98-digit number)

18005572767984851466…97819393751914242559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.800 × 10⁹⁷(98-digit number)

18005572767984851466…97819393751914242561

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

3.601 × 10⁹⁷(98-digit number)

36011145535969702932…95638787503828485119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.601 × 10⁹⁷(98-digit number)

36011145535969702932…95638787503828485121

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

7.202 × 10⁹⁷(98-digit number)

72022291071939405865…91277575007656970239

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