Block #475,340

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 4:25:24 AM · Difficulty 10.4558 · 6,331,234 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70ce6da23bc6e1be163b413219f1e27f0058405ab87553ba5e63106aa51f2a96

View on Chainz ↗

Height

#475,340

Difficulty

10.455777

Transactions

Size

901 B

Version

Bits

0a74add4

Nonce

202,643

Timestamp

4/5/2014, 4:25:24 AM

Confirmations

6,331,234

Mined by

⛏️ @aS?eAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

a4858337d9510cf7e1b6f7bc1075dc23d2320d787a3305184353feb2041a404b

Transactions (1)

Coinbasea4858337d9510c…53feb2041a404b

1 in → 22 out9.1250 XPM811 B

AQvZBsUo…hppgRZTJ AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AMm3qeod…8PBiCMXU

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.

3.587 × 10⁹⁴(95-digit number)

35873491107168477015…99034553701457731199

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

3.587 × 10⁹⁴(95-digit number)

35873491107168477015…99034553701457731199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.587 × 10⁹⁴(95-digit number)

35873491107168477015…99034553701457731201

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

7.174 × 10⁹⁴(95-digit number)

71746982214336954031…98069107402915462399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.174 × 10⁹⁴(95-digit number)

71746982214336954031…98069107402915462401

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

1.434 × 10⁹⁵(96-digit number)

14349396442867390806…96138214805830924799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.434 × 10⁹⁵(96-digit number)

14349396442867390806…96138214805830924801

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

2.869 × 10⁹⁵(96-digit number)

28698792885734781612…92276429611661849599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.869 × 10⁹⁵(96-digit number)

28698792885734781612…92276429611661849601

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

5.739 × 10⁹⁵(96-digit number)

57397585771469563225…84552859223323699199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.739 × 10⁹⁵(96-digit number)

57397585771469563225…84552859223323699201

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 #475,340

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