Block #394,261

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/7/2014, 6:49:02 PM · Difficulty 10.4315 · 6,414,304 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5bfc5ff6ac92c0451029723c927436921e8e040afb992dff9e0d382433b39985

View on Chainz ↗

Height

#394,261

Difficulty

10.431485

Transactions

Size

1.28 KB

Version

Bits

0a6e75c5

Nonce

134,625

Timestamp

2/7/2014, 6:49:02 PM

Confirmations

6,414,304

Mined by

⛏️ aR*vAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9143c48b2af3218980b5d4db25d19900955c601987924fed8cca0022da7764be

Transactions (2)

Coinbase78409764d81b78…bf09ad7ceac0ea

1 in → 23 out9.1800 XPM845 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

aaf70ada1b2f93…75f303eae00777

2 in → 2 out6.1313 XPM374 B

APVe9Ndp…QXjhNzJ8 ARef56Zy…Y46xjgYw

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.

4.134 × 10⁹⁷(98-digit number)

41346738262760264999…92937545278996338879

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

4.134 × 10⁹⁷(98-digit number)

41346738262760264999…92937545278996338879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.134 × 10⁹⁷(98-digit number)

41346738262760264999…92937545278996338881

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

8.269 × 10⁹⁷(98-digit number)

82693476525520529999…85875090557992677759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.269 × 10⁹⁷(98-digit number)

82693476525520529999…85875090557992677761

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

1.653 × 10⁹⁸(99-digit number)

16538695305104105999…71750181115985355519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.653 × 10⁹⁸(99-digit number)

16538695305104105999…71750181115985355521

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

3.307 × 10⁹⁸(99-digit number)

33077390610208211999…43500362231970711039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.307 × 10⁹⁸(99-digit number)

33077390610208211999…43500362231970711041

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

6.615 × 10⁹⁸(99-digit number)

66154781220416423999…87000724463941422079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.615 × 10⁹⁸(99-digit number)

66154781220416423999…87000724463941422081

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 #394,261

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