Block #476,468

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 8:38:45 PM · Difficulty 10.4727 · 6,326,594 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

74d0bfa647263dc1d9d73e54d5f3ecd78ff919c47d139b31afe0faed22995567

View on Chainz ↗

Height

#476,468

Difficulty

10.472729

Transactions

Size

1.06 KB

Version

Bits

0a7904c6

Nonce

3,227

Timestamp

4/5/2014, 8:38:45 PM

Confirmations

6,326,594

Mined by

⛏️ 4EAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

118829ec9a5c71f48f3930bc01eeebfccde03860597facb950e7717596932757

Transactions (4)

Coinbase63beb9c960f3dc…50775ef3414ce3

1 in → 3 out9.1300 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

5c77f7e2ae1e10…c67f934aedd110

1 in → 2 out5.5824 XPM226 B

AGoNi5MG…ZDc5F7vQ AbA4BoJf…VER8LWCq

d3fea10380fb5d…f343d5134f7770

1 in → 2 out1.4335 XPM227 B

AKbRH1in…XECPkTjL AWaxTsag…PL1cyPDP

a65294a54fb81e…9988e51149be1e

2 in → 2 out1.0880 XPM376 B

AbkDKWUt…ik8Jwo7S ALn6EpnX…MDWN394e

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.

1.720 × 10⁹⁶(97-digit number)

17200786756173297992…05554005468325720319

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

1.720 × 10⁹⁶(97-digit number)

17200786756173297992…05554005468325720319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.720 × 10⁹⁶(97-digit number)

17200786756173297992…05554005468325720321

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

3.440 × 10⁹⁶(97-digit number)

34401573512346595985…11108010936651440639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.440 × 10⁹⁶(97-digit number)

34401573512346595985…11108010936651440641

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

6.880 × 10⁹⁶(97-digit number)

68803147024693191970…22216021873302881279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.880 × 10⁹⁶(97-digit number)

68803147024693191970…22216021873302881281

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

1.376 × 10⁹⁷(98-digit number)

13760629404938638394…44432043746605762559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.376 × 10⁹⁷(98-digit number)

13760629404938638394…44432043746605762561

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

2.752 × 10⁹⁷(98-digit number)

27521258809877276788…88864087493211525119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.752 × 10⁹⁷(98-digit number)

27521258809877276788…88864087493211525121

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