Block #454,381

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/21/2014, 9:29:04 PM · Difficulty 10.3998 · 6,353,631 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ac6c510f66e8262e90edd575170cb9622ba5705728d7b0b7d14d36a80d2e1f1e

View on Chainz ↗

Height

#454,381

Difficulty

10.399817

Transactions

Size

1.26 KB

Version

Bits

0a665a69

Nonce

451,586

Timestamp

3/21/2014, 9:29:04 PM

Confirmations

6,353,631

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

d7e46989d7a335b418677e4d5fefa795d1ac65b82fffd3c9acc278bf6c492eb2

Transactions (3)

Coinbase9d3f055b0ee735…7c171efb5ef8e8

1 in → 4 out9.2500 XPM199 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN Aa2Amg89…4rjYrsPZ AJno7LX2…vo4wdWtY

27808cb2ec8537…846c598ec9439f

3 in → 2 out288.4102 XPM522 B

ANz6j3Dq…mZpcYZXq AN8MWfEq…BKtKDjBS

00a279c728751e…ed261e53092afa

2 in → 7 out18.5100 XPM478 B

AFqwEJFf…zqg3ZgE6 AWjvkJwz…JbcQNttY APd3tden…qhRE2ARG AZwXBq4j…rzStTzBk AVrzMBgN…EVKZMzxb

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.

1.123 × 10⁹⁵(96-digit number)

11230301627376453468…92433611265991915519

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

1.123 × 10⁹⁵(96-digit number)

11230301627376453468…92433611265991915519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.123 × 10⁹⁵(96-digit number)

11230301627376453468…92433611265991915521

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

2.246 × 10⁹⁵(96-digit number)

22460603254752906936…84867222531983831039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.246 × 10⁹⁵(96-digit number)

22460603254752906936…84867222531983831041

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

4.492 × 10⁹⁵(96-digit number)

44921206509505813873…69734445063967662079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.492 × 10⁹⁵(96-digit number)

44921206509505813873…69734445063967662081

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

8.984 × 10⁹⁵(96-digit number)

89842413019011627747…39468890127935324159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.984 × 10⁹⁵(96-digit number)

89842413019011627747…39468890127935324161

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

1.796 × 10⁹⁶(97-digit number)

17968482603802325549…78937780255870648319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.796 × 10⁹⁶(97-digit number)

17968482603802325549…78937780255870648321

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 #454,381

Cookie Preferences