Block #450,788

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/19/2014, 12:30:23 PM · Difficulty 10.3768 · 6,376,326 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94bbf65807f6236506f4d0ffa7e7c276c1189f02a15e511b01490658a9c328ca

View on Chainz ↗

Height

#450,788

Difficulty

10.376791

Transactions

Size

969 B

Version

Bits

0a607561

Nonce

87,183

Timestamp

3/19/2014, 12:30:23 PM

Confirmations

6,376,326

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9d2e956368ea71974ac0dab952abddd9cf89ca5b00c7bb45e91c4333d5431e6c

Transactions (1)

Coinbase9d2e956368ea71…1c4333d5431e6c

1 in → 24 out9.2700 XPM879 B

AQvZBsUo…hppgRZTJ AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 AWMrD5hP…ZwsoxvZ3 ALqxX1WA…hsKjbnXn

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.

3.674 × 10⁹⁵(96-digit number)

36743406097043397003…32902810045909693439

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

3.674 × 10⁹⁵(96-digit number)

36743406097043397003…32902810045909693439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.674 × 10⁹⁵(96-digit number)

36743406097043397003…32902810045909693441

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

7.348 × 10⁹⁵(96-digit number)

73486812194086794007…65805620091819386879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.348 × 10⁹⁵(96-digit number)

73486812194086794007…65805620091819386881

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

1.469 × 10⁹⁶(97-digit number)

14697362438817358801…31611240183638773759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.469 × 10⁹⁶(97-digit number)

14697362438817358801…31611240183638773761

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

2.939 × 10⁹⁶(97-digit number)

29394724877634717602…63222480367277547519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.939 × 10⁹⁶(97-digit number)

29394724877634717602…63222480367277547521

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

5.878 × 10⁹⁶(97-digit number)

58789449755269435205…26444960734555095039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.878 × 10⁹⁶(97-digit number)

58789449755269435205…26444960734555095041

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 #450,788

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