Block #379,606

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 3:33:14 PM · Difficulty 10.4198 · 6,436,614 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0bcfce113634b207768afd8d6cb4f8c7414d3d3a184fe48a0193942fb38f426d

View on Chainz ↗

Height

#379,606

Difficulty

10.419810

Transactions

Size

882 B

Version

Bits

0a6b78a6

Nonce

65,983

Timestamp

1/28/2014, 3:33:14 PM

Confirmations

6,436,614

Mined by

⛏️ P2SHAZVnc7iGdXD8aVz8GUQXuxoV79jVjHLzCS

Merkle Root

7f27f1681422ec708f22f9bc1d27cecb6df2c184b72df0573a52f06b72134423

Transactions (4)

Coinbase2b0f5ca71a4220…c52333648a1557

1 in → 1 out9.2300 XPM109 B

AZVnc7iG…jVjHLzCS

658f690bd79576…5fb2376447a0f8

1 in → 2 out6.1078 XPM227 B

AG8m4yVR…5HBobTKU AZoumwwt…qyvNAj6W

a44dace12c8a5e…6198a767a81a76

1 in → 2 out6.0549 XPM227 B

ARi8Wk6S…RJkCuKVy AVuEzmJt…LGErqmd9

bdd11b64f2a63a…b3add162d54604

1 in → 2 out4.1036 XPM227 B

AYXiQEyP…myu8sEHZ AJbQMoXi…z1GZnBwc

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.

3.161 × 10⁹⁸(99-digit number)

31611370988973108367…03114332911170153199

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

3.161 × 10⁹⁸(99-digit number)

31611370988973108367…03114332911170153199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.161 × 10⁹⁸(99-digit number)

31611370988973108367…03114332911170153201

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

6.322 × 10⁹⁸(99-digit number)

63222741977946216735…06228665822340306399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.322 × 10⁹⁸(99-digit number)

63222741977946216735…06228665822340306401

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

1.264 × 10⁹⁹(100-digit number)

12644548395589243347…12457331644680612799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.264 × 10⁹⁹(100-digit number)

12644548395589243347…12457331644680612801

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

2.528 × 10⁹⁹(100-digit number)

25289096791178486694…24914663289361225599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.528 × 10⁹⁹(100-digit number)

25289096791178486694…24914663289361225601

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

5.057 × 10⁹⁹(100-digit number)

50578193582356973388…49829326578722451199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.057 × 10⁹⁹(100-digit number)

50578193582356973388…49829326578722451201

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 #379,606

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