Block #437,251

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2014, 4:18:30 AM · Difficulty 10.3582 · 6,379,502 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e82c5d7df9fcc6be707529bd2985a1f30be31dab54876c408f08ba748174a21f

View on Chainz ↗

Height

#437,251

Difficulty

10.358182

Transactions

Size

1003 B

Version

Bits

0a5bb1d9

Nonce

22,091

Timestamp

3/10/2014, 4:18:30 AM

Confirmations

6,379,502

Mined by

⛏️ aS<AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e820e7e9adea80991dd0db2bfc6493e080b8dd42ba9b3839e677eec8511aca90

Transactions (1)

Coinbasee820e7e9adea80…77eec8511aca90

1 in → 25 out9.3100 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGD4yZQw…hGzM2XAx ATKK7iFz…wZm46KN1 AScAzqGc…BZ6tV1vJ

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.

2.750 × 10⁹⁵(96-digit number)

27509033120781508863…05228539912932447319

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

2.750 × 10⁹⁵(96-digit number)

27509033120781508863…05228539912932447319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.750 × 10⁹⁵(96-digit number)

27509033120781508863…05228539912932447321

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

5.501 × 10⁹⁵(96-digit number)

55018066241563017727…10457079825864894639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.501 × 10⁹⁵(96-digit number)

55018066241563017727…10457079825864894641

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

1.100 × 10⁹⁶(97-digit number)

11003613248312603545…20914159651729789279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.100 × 10⁹⁶(97-digit number)

11003613248312603545…20914159651729789281

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

2.200 × 10⁹⁶(97-digit number)

22007226496625207090…41828319303459578559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.200 × 10⁹⁶(97-digit number)

22007226496625207090…41828319303459578561

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

4.401 × 10⁹⁶(97-digit number)

44014452993250414181…83656638606919157119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.401 × 10⁹⁶(97-digit number)

44014452993250414181…83656638606919157121

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 #437,251

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