Block #392,241

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2014, 8:18:56 AM · Difficulty 10.4365 · 6,412,575 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fafce943fd00fc28d4288f3c1dc00c0e1162ea872b3fb615bbf9542d154e63c3

View on Chainz ↗

Height

#392,241

Difficulty

10.436540

Transactions

Size

867 B

Version

Bits

0a6fc10e

Nonce

34,819

Timestamp

2/6/2014, 8:18:56 AM

Confirmations

6,412,575

Mined by

⛏️ 1aRErPAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

a581c5f27ac0292caf2972f92a76e1ae17bb6f683987b324d4ed488637ee9413

Transactions (1)

Coinbasea581c5f27ac029…ed488637ee9413

1 in → 21 out9.1700 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

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.

4.176 × 10⁹⁵(96-digit number)

41766340365501344726…71944941823611503319

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

4.176 × 10⁹⁵(96-digit number)

41766340365501344726…71944941823611503319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.176 × 10⁹⁵(96-digit number)

41766340365501344726…71944941823611503321

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

8.353 × 10⁹⁵(96-digit number)

83532680731002689452…43889883647223006639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.353 × 10⁹⁵(96-digit number)

83532680731002689452…43889883647223006641

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

1.670 × 10⁹⁶(97-digit number)

16706536146200537890…87779767294446013279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.670 × 10⁹⁶(97-digit number)

16706536146200537890…87779767294446013281

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

3.341 × 10⁹⁶(97-digit number)

33413072292401075780…75559534588892026559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.341 × 10⁹⁶(97-digit number)

33413072292401075780…75559534588892026561

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

6.682 × 10⁹⁶(97-digit number)

66826144584802151561…51119069177784053119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.682 × 10⁹⁶(97-digit number)

66826144584802151561…51119069177784053121

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