Block #446,023

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2014, 6:59:55 AM · Difficulty 10.3598 · 6,359,667 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fefffe1089c8daf1958821430dae23fbb814b713e0f90a66954e628167f45161

View on Chainz ↗

Height

#446,023

Difficulty

10.359827

Transactions

Size

902 B

Version

Bits

0a5c1d9e

Nonce

240,169

Timestamp

3/16/2014, 6:59:55 AM

Confirmations

6,359,667

Mined by

⛏️ GaS%KAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ab6ec8e38857dd858a80580adcb4003dad5cef2f6c9bc2ee50e47c6fbf1c15d0

Transactions (1)

Coinbaseab6ec8e38857dd…e47c6fbf1c15d0

1 in → 22 out9.2975 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq

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.

1.453 × 10⁹⁷(98-digit number)

14530021319339661732…03192536950849736959

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

1.453 × 10⁹⁷(98-digit number)

14530021319339661732…03192536950849736959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.453 × 10⁹⁷(98-digit number)

14530021319339661732…03192536950849736961

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

2.906 × 10⁹⁷(98-digit number)

29060042638679323465…06385073901699473919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.906 × 10⁹⁷(98-digit number)

29060042638679323465…06385073901699473921

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

5.812 × 10⁹⁷(98-digit number)

58120085277358646930…12770147803398947839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.812 × 10⁹⁷(98-digit number)

58120085277358646930…12770147803398947841

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

1.162 × 10⁹⁸(99-digit number)

11624017055471729386…25540295606797895679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.162 × 10⁹⁸(99-digit number)

11624017055471729386…25540295606797895681

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

2.324 × 10⁹⁸(99-digit number)

23248034110943458772…51080591213595791359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.324 × 10⁹⁸(99-digit number)

23248034110943458772…51080591213595791361

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