Block #454,181

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/21/2014, 6:40:03 PM · Difficulty 10.3958 · 6,352,356 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

54b9d8693d53049bf052428de0b74d8969d25e370c763a3973552052653d3f18

View on Chainz ↗

Height

#454,181

Difficulty

10.395774

Transactions

Size

970 B

Version

Bits

0a65516f

Nonce

4,349

Timestamp

3/21/2014, 6:40:03 PM

Confirmations

6,352,356

Mined by

⛏️ %aS,hsAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

db3b06f688a6c775f6fd02982ecae3231b492186fa4c4c1e08962a137d6e30d5

Transactions (1)

Coinbasedb3b06f688a6c7…962a137d6e30d5

1 in → 24 out9.2400 XPM879 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF AScAzqGc…BZ6tV1vJ ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq

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.

2.702 × 10⁹⁷(98-digit number)

27023058093939774486…40908091907425688319

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

2.702 × 10⁹⁷(98-digit number)

27023058093939774486…40908091907425688319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.702 × 10⁹⁷(98-digit number)

27023058093939774486…40908091907425688321

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

5.404 × 10⁹⁷(98-digit number)

54046116187879548972…81816183814851376639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.404 × 10⁹⁷(98-digit number)

54046116187879548972…81816183814851376641

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

1.080 × 10⁹⁸(99-digit number)

10809223237575909794…63632367629702753279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.080 × 10⁹⁸(99-digit number)

10809223237575909794…63632367629702753281

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

2.161 × 10⁹⁸(99-digit number)

21618446475151819589…27264735259405506559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.161 × 10⁹⁸(99-digit number)

21618446475151819589…27264735259405506561

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

4.323 × 10⁹⁸(99-digit number)

43236892950303639178…54529470518811013119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.323 × 10⁹⁸(99-digit number)

43236892950303639178…54529470518811013121

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 #454,181

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