Block #446,182

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2014, 9:23:32 AM · Difficulty 10.3617 · 6,357,497 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70cb28b6e480abe72df1d203bd6c1292010e4cb7a1d912dee7899ee00304031b

View on Chainz ↗

Height

#446,182

Difficulty

10.361671

Transactions

Size

1.32 KB

Version

Bits

0a5c967c

Nonce

72,240

Timestamp

3/16/2014, 9:23:32 AM

Confirmations

6,357,497

Mined by

⛏️ aS%mAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5fa23e9d6a031ec3eccd6ab99a63a8e8d7b07d2580deb990b7dc3f181d160424

Transactions (2)

Coinbase3b261cdb76d140…e0f4d525e1cee3

1 in → 20 out9.3000 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq

664e370e5e2d0e…a5a9b88d5f6d00

3 in → 2 out30.0101 XPM520 B

ALADBzoA…UX3rRXrS AQupavW6…boFysxqU

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.

3.609 × 10⁹⁷(98-digit number)

36093821028569912550…72752075835430584319

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

3.609 × 10⁹⁷(98-digit number)

36093821028569912550…72752075835430584319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.609 × 10⁹⁷(98-digit number)

36093821028569912550…72752075835430584321

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

7.218 × 10⁹⁷(98-digit number)

72187642057139825101…45504151670861168639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.218 × 10⁹⁷(98-digit number)

72187642057139825101…45504151670861168641

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

1.443 × 10⁹⁸(99-digit number)

14437528411427965020…91008303341722337279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.443 × 10⁹⁸(99-digit number)

14437528411427965020…91008303341722337281

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

2.887 × 10⁹⁸(99-digit number)

28875056822855930040…82016606683444674559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.887 × 10⁹⁸(99-digit number)

28875056822855930040…82016606683444674561

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

5.775 × 10⁹⁸(99-digit number)

57750113645711860081…64033213366889349119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.775 × 10⁹⁸(99-digit number)

57750113645711860081…64033213366889349121

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