Block #273,463

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 7:45:33 PM · Difficulty 9.9549 · 6,553,508 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

21f0651a7ee27a12725a87e5e93a892b43bd96f24fef8fb9095fad7364972366

View on Chainz ↗

Height

#273,463

Difficulty

9.954921

Transactions

Size

1.15 KB

Version

Bits

09f475b6

Nonce

9,554

Timestamp

11/25/2013, 7:45:33 PM

Confirmations

6,553,508

Mined by

⛏️ 7,aRAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

85a4e9dbc5d54a60611d41c727eff113b981c7e78007325da95fa0625d42a6cf

Transactions (1)

Coinbase85a4e9dbc5d54a…5fa0625d42a6cf

1 in → 30 out10.0600 XPM1.06 KB

APeshfYV…3PKcKMKH AJ583KJv…3M16nmdw AN8nUzff…YcDfRDQ2 Ac5sZcdP…kzV4eckG APvpz12N…NjdsxTYA

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.

1.921 × 10⁹⁴(95-digit number)

19219679550094712292…24461786493722542079

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

1.921 × 10⁹⁴(95-digit number)

19219679550094712292…24461786493722542079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.921 × 10⁹⁴(95-digit number)

19219679550094712292…24461786493722542081

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

3.843 × 10⁹⁴(95-digit number)

38439359100189424585…48923572987445084159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.843 × 10⁹⁴(95-digit number)

38439359100189424585…48923572987445084161

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

7.687 × 10⁹⁴(95-digit number)

76878718200378849170…97847145974890168319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.687 × 10⁹⁴(95-digit number)

76878718200378849170…97847145974890168321

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

1.537 × 10⁹⁵(96-digit number)

15375743640075769834…95694291949780336639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.537 × 10⁹⁵(96-digit number)

15375743640075769834…95694291949780336641

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

3.075 × 10⁹⁵(96-digit number)

30751487280151539668…91388583899560673279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #273,463

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