Block #443,045

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 7:06:12 AM · Difficulty 10.3440 · 6,363,818 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f6b4647a4b6fcfd9b26f12f7213ad2d46c0cf2889134ce2b4caeb3547ca90c2

View on Chainz ↗

Height

#443,045

Difficulty

10.344049

Transactions

Size

901 B

Version

Bits

0a581390

Nonce

86,683

Timestamp

3/14/2014, 7:06:12 AM

Confirmations

6,363,818

Mined by

⛏️ aS"9AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e1feceedf2d5854e4779ba6a906236478981f27182bd7be7c60bc42eec167c1e

Transactions (1)

Coinbasee1feceedf2d585…0bc42eec167c1e

1 in → 22 out9.3300 XPM811 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1

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.

5.413 × 10⁹⁵(96-digit number)

54133585074601403482…85695294006107927039

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

5.413 × 10⁹⁵(96-digit number)

54133585074601403482…85695294006107927039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.413 × 10⁹⁵(96-digit number)

54133585074601403482…85695294006107927041

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

1.082 × 10⁹⁶(97-digit number)

10826717014920280696…71390588012215854079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.082 × 10⁹⁶(97-digit number)

10826717014920280696…71390588012215854081

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

2.165 × 10⁹⁶(97-digit number)

21653434029840561393…42781176024431708159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.165 × 10⁹⁶(97-digit number)

21653434029840561393…42781176024431708161

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

4.330 × 10⁹⁶(97-digit number)

43306868059681122786…85562352048863416319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.330 × 10⁹⁶(97-digit number)

43306868059681122786…85562352048863416321

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

8.661 × 10⁹⁶(97-digit number)

86613736119362245572…71124704097726832639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.661 × 10⁹⁶(97-digit number)

86613736119362245572…71124704097726832641

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 #443,045

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