Block #437,247

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2014, 4:17:45 AM · Difficulty 10.3579 · 6,373,426 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0268cd48e1a21609e1d8aea2e767eb5c61ebbc92188827739b5e78aa4e65ced2

View on Chainz ↗

Height

#437,247

Difficulty

10.357881

Transactions

Size

971 B

Version

Bits

0a5b9e15

Nonce

51,599

Timestamp

3/10/2014, 4:17:45 AM

Confirmations

6,373,426

Mined by

⛏️ aS<ymAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

40681b05753bcb36ee4782995b764d453576ac497b642636fc80ed2bbf12d001

Transactions (1)

Coinbase40681b05753bcb…80ed2bbf12d001

1 in → 24 out9.3100 XPM879 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.

2.282 × 10⁹⁸(99-digit number)

22820167007158870155…38021494653850828799

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

2.282 × 10⁹⁸(99-digit number)

22820167007158870155…38021494653850828799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.282 × 10⁹⁸(99-digit number)

22820167007158870155…38021494653850828801

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

4.564 × 10⁹⁸(99-digit number)

45640334014317740310…76042989307701657599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.564 × 10⁹⁸(99-digit number)

45640334014317740310…76042989307701657601

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

9.128 × 10⁹⁸(99-digit number)

91280668028635480620…52085978615403315199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.128 × 10⁹⁸(99-digit number)

91280668028635480620…52085978615403315201

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

1.825 × 10⁹⁹(100-digit number)

18256133605727096124…04171957230806630399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.825 × 10⁹⁹(100-digit number)

18256133605727096124…04171957230806630401

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

3.651 × 10⁹⁹(100-digit number)

36512267211454192248…08343914461613260799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.651 × 10⁹⁹(100-digit number)

36512267211454192248…08343914461613260801

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 #437,247

Cookie Preferences