Block #443,922

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 9:39:31 PM · Difficulty 10.3464 · 6,351,818 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b1eab56c13128034eeab0257279bbbda00aed6af333106534d0e33ab72b27c80

View on Chainz ↗

Height

#443,922

Difficulty

10.346391

Transactions

Size

1.47 KB

Version

Bits

0a58ad11

Nonce

378,970

Timestamp

3/14/2014, 9:39:31 PM

Confirmations

6,351,818

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c8b1c06637c3b42dd9c1746acfe77c635c09a2c8b05890e627c537337e085620

Transactions (2)

Coinbase80a3d4b832f2d1…15bfd3800b65a8

1 in → 1 out9.3500 XPM110 B

AeKNrjNj…1NEq95Ta

b472ee9fcc5a68…e591ad9ff1f8b7

6 in → 18 out55.9400 XPM1.28 KB

Ac7njVur…DfY6Hpwr AJzVd5zU…kkWV5Svn AaSUNzJU…2iWckcUK AJ1Rg4tk…5YkqEmTH AMw6Dcr2…pMu8K6Zs

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.

4.145 × 10⁹⁸(99-digit number)

41452524430081822296…15989782213655592319

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

4.145 × 10⁹⁸(99-digit number)

41452524430081822296…15989782213655592319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.145 × 10⁹⁸(99-digit number)

41452524430081822296…15989782213655592321

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

8.290 × 10⁹⁸(99-digit number)

82905048860163644592…31979564427311184639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.290 × 10⁹⁸(99-digit number)

82905048860163644592…31979564427311184641

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

1.658 × 10⁹⁹(100-digit number)

16581009772032728918…63959128854622369279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.658 × 10⁹⁹(100-digit number)

16581009772032728918…63959128854622369281

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

3.316 × 10⁹⁹(100-digit number)

33162019544065457837…27918257709244738559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.316 × 10⁹⁹(100-digit number)

33162019544065457837…27918257709244738561

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

6.632 × 10⁹⁹(100-digit number)

66324039088130915674…55836515418489477119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.632 × 10⁹⁹(100-digit number)

66324039088130915674…55836515418489477121

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