Block #192,226

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/3/2013, 5:31:13 PM · Difficulty 9.8746 · 6,611,380 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ba29184ccb4db2e4cf5f66e7155178a5494f44ffbe212828d985408e21e008de

View on Chainz ↗

Height

#192,226

Difficulty

9.874627

Transactions

Size

2.62 KB

Version

Bits

09dfe791

Nonce

1,164,892,398

Timestamp

10/3/2013, 5:31:13 PM

Confirmations

6,611,380

Mined by

⛏️ RMAKF2rJVd4KA4geKnHkAUrdbDEWfNsDgS32

Merkle Root

1523371818354ebc199b75dca2b2c4735624f0c1fabf1b376e11d80421ee5bc9

Transactions (2)

Coinbase3f368fcc9ded60…5ac8dcb167d51a

1 in → 59 out10.2200 XPM2.02 KB

AKF2rJVd…fNsDgS32 AU7kLmhQ…qhCn5tjQ AGT9hnPx…C3sxd5B5 AKoHGbXL…AMALbdsK AKRpbXWP…X6DRYUqb

5264ace4b502f5…8b687f7b0659b6

3 in → 2 out10.3646 XPM523 B

ALpthvGg…D1g5z4CT AMzSQuDj…Xka7epJa

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.

1.413 × 10⁹⁸(99-digit number)

14139104694438803263…98656268472430719359

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

1.413 × 10⁹⁸(99-digit number)

14139104694438803263…98656268472430719359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.413 × 10⁹⁸(99-digit number)

14139104694438803263…98656268472430719361

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

2.827 × 10⁹⁸(99-digit number)

28278209388877606527…97312536944861438719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.827 × 10⁹⁸(99-digit number)

28278209388877606527…97312536944861438721

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

5.655 × 10⁹⁸(99-digit number)

56556418777755213054…94625073889722877439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.655 × 10⁹⁸(99-digit number)

56556418777755213054…94625073889722877441

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

1.131 × 10⁹⁹(100-digit number)

11311283755551042610…89250147779445754879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.131 × 10⁹⁹(100-digit number)

11311283755551042610…89250147779445754881

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

2.262 × 10⁹⁹(100-digit number)

22622567511102085221…78500295558891509759

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