Block #487,543

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2014, 5:21:55 AM · Difficulty 10.6417 · 6,317,610 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f869cbc0ad7c646d4b76f5e540ff230abc25b9c60d614dce334ce27ca05dc731

View on Chainz ↗

Height

#487,543

Difficulty

10.641680

Transactions

Size

865 B

Version

Bits

0aa44527

Nonce

637,679

Timestamp

4/12/2014, 5:21:55 AM

Confirmations

6,317,610

Mined by

⛏️ wpaSHAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f1cc493ae1496a1f2d71ef522990daead99bfac08edaca984cda167d81431b3c

Transactions (1)

Coinbasef1cc493ae1496a…da167d81431b3c

1 in → 21 out8.8200 XPM777 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j

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.

4.585 × 10⁹⁰(91-digit number)

45853218082886914331…07357007026526937039

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

4.585 × 10⁹⁰(91-digit number)

45853218082886914331…07357007026526937039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.585 × 10⁹⁰(91-digit number)

45853218082886914331…07357007026526937041

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

9.170 × 10⁹⁰(91-digit number)

91706436165773828663…14714014053053874079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.170 × 10⁹⁰(91-digit number)

91706436165773828663…14714014053053874081

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

1.834 × 10⁹¹(92-digit number)

18341287233154765732…29428028106107748159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.834 × 10⁹¹(92-digit number)

18341287233154765732…29428028106107748161

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

3.668 × 10⁹¹(92-digit number)

36682574466309531465…58856056212215496319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.668 × 10⁹¹(92-digit number)

36682574466309531465…58856056212215496321

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

7.336 × 10⁹¹(92-digit number)

73365148932619062931…17712112424430992639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.336 × 10⁹¹(92-digit number)

73365148932619062931…17712112424430992641

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