Block #444,974

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 2:27:24 PM · Difficulty 10.3525 · 6,354,385 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be4b7df57c715596f30ca9d8e4ebc6036da4cb174fac866361527c5bfef8883b

View on Chainz ↗

Height

#444,974

Difficulty

10.352460

Transactions

Size

937 B

Version

Bits

0a5a3ad6

Nonce

6,276

Timestamp

3/15/2014, 2:27:24 PM

Confirmations

6,354,385

Mined by

⛏️ .aS$bAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ca6699ce3244f1db51e589903a309c18c67fdca5257091c8907c8ba3fcfcf91e

Transactions (1)

Coinbaseca6699ce3244f1…7c8ba3fcfcf91e

1 in → 23 out9.3200 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AdhWfaX2…aX7YvEJq AcABUaNj…WXyu2did

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.

3.656 × 10⁹⁸(99-digit number)

36566037997681693093…14067766339623991959

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

3.656 × 10⁹⁸(99-digit number)

36566037997681693093…14067766339623991959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.656 × 10⁹⁸(99-digit number)

36566037997681693093…14067766339623991961

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

7.313 × 10⁹⁸(99-digit number)

73132075995363386186…28135532679247983919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.313 × 10⁹⁸(99-digit number)

73132075995363386186…28135532679247983921

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

1.462 × 10⁹⁹(100-digit number)

14626415199072677237…56271065358495967839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.462 × 10⁹⁹(100-digit number)

14626415199072677237…56271065358495967841

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

2.925 × 10⁹⁹(100-digit number)

29252830398145354474…12542130716991935679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.925 × 10⁹⁹(100-digit number)

29252830398145354474…12542130716991935681

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

5.850 × 10⁹⁹(100-digit number)

58505660796290708949…25084261433983871359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.850 × 10⁹⁹(100-digit number)

58505660796290708949…25084261433983871361

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