Block #444,395

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 5:57:32 AM · Difficulty 10.3430 · 6,380,454 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6456a3e4dd2d5f1ee4c86571d5494c5948f682b476ab228b0ee5bc04df56416a

View on Chainz ↗

Height

#444,395

Difficulty

10.343026

Transactions

Size

7.31 KB

Version

Bits

0a57d090

Nonce

5,429

Timestamp

3/15/2014, 5:57:32 AM

Confirmations

6,380,454

Mined by

⛏️ P2SHATT1LrksMKWQDhN23LH1mWeRZ2oSGe8XsW

Merkle Root

99d029c431f7bb81b0b0bc1b712326d9e0d083474aa7b9b8aa3860bcd6c5fae8

Transactions (4)

Coinbasec7db0cad0ea87e…0e4824a57a7c04

1 in → 1 out9.4200 XPM112 B

ATT1Lrks…oSGe8XsW

489b6f1526890f…47f6e21453c256

5 in → 13 out40.5312 XPM1.03 KB

Aci4Svoj…v721q3U5 AXXCb1i7…kWAn6CzC ANU8S1BR…65yNoREy AT2geRKN…2KpaZBWW ANFpe7j9…DDEt116M

b81c44747ea904…d7b30b47922108

4 in → 2 out6.0361 XPM669 B

AbTEwM2P…rkjrEiz1 AWJJqCR4…JW1deAkn

48a0fbef2162cb…ba9a09db7d00bf

37 in → 2 out12.0261 XPM5.42 KB

Ab9X7nbm…uAdZKWaw AX32q3uJ…ZpKTUZ4U

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.

2.745 × 10⁹⁸(99-digit number)

27450355554624734506…87986595852001222399

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

2.745 × 10⁹⁸(99-digit number)

27450355554624734506…87986595852001222399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.745 × 10⁹⁸(99-digit number)

27450355554624734506…87986595852001222401

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

5.490 × 10⁹⁸(99-digit number)

54900711109249469013…75973191704002444799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.490 × 10⁹⁸(99-digit number)

54900711109249469013…75973191704002444801

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

1.098 × 10⁹⁹(100-digit number)

10980142221849893802…51946383408004889599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.098 × 10⁹⁹(100-digit number)

10980142221849893802…51946383408004889601

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

2.196 × 10⁹⁹(100-digit number)

21960284443699787605…03892766816009779199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.196 × 10⁹⁹(100-digit number)

21960284443699787605…03892766816009779201

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

4.392 × 10⁹⁹(100-digit number)

43920568887399575210…07785533632019558399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.392 × 10⁹⁹(100-digit number)

43920568887399575210…07785533632019558401

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 #444,395

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