Block #487,443

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2014, 3:52:24 AM · Difficulty 10.6408 · 6,322,279 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a81158bc0c7e8bef581793f8eb0969a557c8c750aaaa0399f2dfd59cac80d746

View on Chainz ↗

Height

#487,443

Difficulty

10.640828

Transactions

Size

902 B

Version

Bits

0aa40d48

Nonce

93,908

Timestamp

4/12/2014, 3:52:24 AM

Confirmations

6,322,279

Mined by

⛏️ paSHYAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

61245b8ce00a39141761f81869bb372a1a104dd32a48da275aacec0ddb5ae720

Transactions (1)

Coinbase61245b8ce00a39…acec0ddb5ae720

1 in → 22 out8.8200 XPM811 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AQ8QAT3J…rCFKuVbR

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.

4.421 × 10⁹⁷(98-digit number)

44216799886436588786…86235375313065349119

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

4.421 × 10⁹⁷(98-digit number)

44216799886436588786…86235375313065349119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.421 × 10⁹⁷(98-digit number)

44216799886436588786…86235375313065349121

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

8.843 × 10⁹⁷(98-digit number)

88433599772873177573…72470750626130698239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.843 × 10⁹⁷(98-digit number)

88433599772873177573…72470750626130698241

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

1.768 × 10⁹⁸(99-digit number)

17686719954574635514…44941501252261396479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.768 × 10⁹⁸(99-digit number)

17686719954574635514…44941501252261396481

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

3.537 × 10⁹⁸(99-digit number)

35373439909149271029…89883002504522792959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.537 × 10⁹⁸(99-digit number)

35373439909149271029…89883002504522792961

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

7.074 × 10⁹⁸(99-digit number)

70746879818298542058…79766005009045585919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.074 × 10⁹⁸(99-digit number)

70746879818298542058…79766005009045585921

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 #487,443

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