Block #272,182

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 2:48:52 AM · Difficulty 9.9525 · 6,523,571 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

829e7f1e00ff789954e38a435913734f07b949df762716c0a66bf58872b9d971

View on Chainz ↗

Height

#272,182

Difficulty

9.952454

Transactions

Size

574 B

Version

Bits

09f3d405

Nonce

50,306

Timestamp

11/25/2013, 2:48:52 AM

Confirmations

6,523,571

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

062286fa383eee20f92ee4939f2e8648cd29b78de949af5e38bdcd8004974fa6

Transactions (2)

Coinbased2889793f49aee…a8caed87a20e6b

1 in → 1 out10.0900 XPM110 B

AeKNrjNj…1NEq95Ta

fbd8704b70216b…398f4e48963d27

2 in → 2 out200.0500 XPM375 B

AWpdyWbs…a4xebwNx AVyuHXCy…Gc1KSpKq

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.

1.297 × 10⁹³(94-digit number)

12970117053909383078…63788672394851843199

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

1.297 × 10⁹³(94-digit number)

12970117053909383078…63788672394851843199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.297 × 10⁹³(94-digit number)

12970117053909383078…63788672394851843201

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

2.594 × 10⁹³(94-digit number)

25940234107818766157…27577344789703686399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.594 × 10⁹³(94-digit number)

25940234107818766157…27577344789703686401

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

5.188 × 10⁹³(94-digit number)

51880468215637532315…55154689579407372799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.188 × 10⁹³(94-digit number)

51880468215637532315…55154689579407372801

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

1.037 × 10⁹⁴(95-digit number)

10376093643127506463…10309379158814745599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.037 × 10⁹⁴(95-digit number)

10376093643127506463…10309379158814745601

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

2.075 × 10⁹⁴(95-digit number)

20752187286255012926…20618758317629491199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.075 × 10⁹⁴(95-digit number)

20752187286255012926…20618758317629491201

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