Block #442,278

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2014, 5:41:01 PM · Difficulty 10.3489 · 6,363,577 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8757fb96f1c05b5503a6db796dc6eaa04f4710f570ce69136f9e9aa6df00c2fd

View on Chainz ↗

Height

#442,278

Difficulty

10.348886

Transactions

Size

971 B

Version

Bits

0a595093

Nonce

11,696

Timestamp

3/13/2014, 5:41:01 PM

Confirmations

6,363,577

Mined by

⛏️ aS!dAAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

2e563f08c25ae3779725e55857f96006cb6880b4b34a24586e2ce7fae4bfd679

Transactions (1)

Coinbase2e563f08c25ae3…2ce7fae4bfd679

1 in → 24 out9.3200 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 AMm3qeod…8PBiCMXU

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.

1.442 × 10⁹⁹(100-digit number)

14427954467237453241…12885069242289817839

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

1.442 × 10⁹⁹(100-digit number)

14427954467237453241…12885069242289817839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.442 × 10⁹⁹(100-digit number)

14427954467237453241…12885069242289817841

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

2.885 × 10⁹⁹(100-digit number)

28855908934474906483…25770138484579635679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.885 × 10⁹⁹(100-digit number)

28855908934474906483…25770138484579635681

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

5.771 × 10⁹⁹(100-digit number)

57711817868949812966…51540276969159271359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.771 × 10⁹⁹(100-digit number)

57711817868949812966…51540276969159271361

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

1.154 × 10¹⁰⁰(101-digit number)

11542363573789962593…03080553938318542719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.154 × 10¹⁰⁰(101-digit number)

11542363573789962593…03080553938318542721

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

2.308 × 10¹⁰⁰(101-digit number)

23084727147579925186…06161107876637085439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.308 × 10¹⁰⁰(101-digit number)

23084727147579925186…06161107876637085441

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