Block #443,124

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 8:24:07 AM · Difficulty 10.3441 · 6,364,622 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f7415981d787834151e848d7142bfd694b4ba0b5e07638b5ccdf3717f233b71d

View on Chainz ↗

Height

#443,124

Difficulty

10.344117

Transactions

Size

1.58 KB

Version

Bits

0a581807

Nonce

506,511

Timestamp

3/14/2014, 8:24:07 AM

Confirmations

6,364,622

Mined by

⛏️ aS"CAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b870fd511ab333fcd4aecfc2de81122f2c3351bedfff2710bee98913295d57a2

Transactions (4)

Coinbase7be3e6b6239fa8…8ed2bcdff49006

1 in → 23 out9.3300 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

c8aadcd8bf630d…dc98ee71504dee

1 in → 2 out6.7253 XPM227 B

ATprbEg4…34D1RYQr AZ9HA5jV…nNrXcwLk

4b93d9d6c51fc4…ca4a787124dff8

1 in → 2 out6.2149 XPM225 B

AR9qLgD4…ieZFLNik ATZCZabL…FHs8ADLe

3263efdbb25fba…f206393da1264a

1 in → 2 out6.2029 XPM225 B

AVATn7b6…QJPv5Hok AXZf8xqq…hQwCQgXt

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.

8.405 × 10⁹⁷(98-digit number)

84053000323402617022…52418269852204126719

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

8.405 × 10⁹⁷(98-digit number)

84053000323402617022…52418269852204126719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.405 × 10⁹⁷(98-digit number)

84053000323402617022…52418269852204126721

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

1.681 × 10⁹⁸(99-digit number)

16810600064680523404…04836539704408253439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.681 × 10⁹⁸(99-digit number)

16810600064680523404…04836539704408253441

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

3.362 × 10⁹⁸(99-digit number)

33621200129361046808…09673079408816506879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.362 × 10⁹⁸(99-digit number)

33621200129361046808…09673079408816506881

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

6.724 × 10⁹⁸(99-digit number)

67242400258722093617…19346158817633013759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.724 × 10⁹⁸(99-digit number)

67242400258722093617…19346158817633013761

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

1.344 × 10⁹⁹(100-digit number)

13448480051744418723…38692317635266027519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.344 × 10⁹⁹(100-digit number)

13448480051744418723…38692317635266027521

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 #443,124

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