Block #392,634

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2014, 2:29:03 PM · Difficulty 10.4387 · 6,415,747 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d59d641360f9ee73106689f2d4c2f3269ae211408ba86e2403922468039c76b

View on Chainz ↗

Height

#392,634

Difficulty

10.438716

Transactions

Size

885 B

Version

Bits

0a704fab

Nonce

31,478

Timestamp

2/6/2014, 2:29:03 PM

Confirmations

6,415,747

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a4f13750df072ed4b88fedcad77277de454611422519be90bf6c223badd5fc14

Transactions (4)

Coinbasef5cacb109f8fa3…d0f104e5359285

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

18c4b97a3ced3e…3319a36296500b

1 in → 2 out3.1458 XPM227 B

ANa4b2yc…KXu3JPWZ AcWvsRjB…91YyLHim

fd5fb2db9d4470…d916167aac32d9

1 in → 2 out2.3627 XPM226 B

AN1yaeRM…hFtW6eGz AYGqAE6f…xNKGvfYR

d95e9df0af3fe0…7813fda13431c2

1 in → 2 out2.1177 XPM227 B

ASbTGAL1…CZKukTjX AdGjXB6X…nEszu4QZ

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.

4.227 × 10⁹¹(92-digit number)

42279957005006255107…57358759421923699759

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

4.227 × 10⁹¹(92-digit number)

42279957005006255107…57358759421923699759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.227 × 10⁹¹(92-digit number)

42279957005006255107…57358759421923699761

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

8.455 × 10⁹¹(92-digit number)

84559914010012510215…14717518843847399519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.455 × 10⁹¹(92-digit number)

84559914010012510215…14717518843847399521

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

1.691 × 10⁹²(93-digit number)

16911982802002502043…29435037687694799039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.691 × 10⁹²(93-digit number)

16911982802002502043…29435037687694799041

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

3.382 × 10⁹²(93-digit number)

33823965604005004086…58870075375389598079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.382 × 10⁹²(93-digit number)

33823965604005004086…58870075375389598081

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

6.764 × 10⁹²(93-digit number)

67647931208010008172…17740150750779196159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.764 × 10⁹²(93-digit number)

67647931208010008172…17740150750779196161

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 #392,634

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