Block #391,616

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/5/2014, 10:33:20 PM · Difficulty 10.4320 · 6,413,727 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7f58eddca27ee18b0e690aa828cf8f9e9e8f293a66bee862b4f1bd5f11a47b2

View on Chainz ↗

Height

#391,616

Difficulty

10.431989

Transactions

Size

4.25 KB

Version

Bits

0a6e96cd

Nonce

25,702

Timestamp

2/5/2014, 10:33:20 PM

Confirmations

6,413,727

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

7e8257f898a67d1fd1298b3d0f30ab55cc41e8c4ff46fd5307dbef70125fe29c

Transactions (4)

Coinbasec2f48e6f0c2748…7a042b9db2bee3

1 in → 21 out9.1700 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AFutDVqJ…TJTJj6UF

7cce55d7e877f9…383c74415d3a29

17 in → 2 out51.3131 XPM2.53 KB

ANEoyD3R…8AvA9i6U ATRsuyen…oNpDLgXh

4302fea4df692c…6d2ed164197532

1 in → 2 out3.0868 XPM226 B

ATS7jojQ…cemQPJ2Z AYb8H7sQ…m86ufYFN

d32394f4e3e674…7a08d75d017148

4 in → 2 out5.2927 XPM669 B

AWhqCNs1…mTz9bU71 AXuFZ9ky…5bVppGoh

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.

6.412 × 10⁹³(94-digit number)

64129609702949604007…96560555503470705079

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

6.412 × 10⁹³(94-digit number)

64129609702949604007…96560555503470705079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.412 × 10⁹³(94-digit number)

64129609702949604007…96560555503470705081

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

1.282 × 10⁹⁴(95-digit number)

12825921940589920801…93121111006941410159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.282 × 10⁹⁴(95-digit number)

12825921940589920801…93121111006941410161

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

2.565 × 10⁹⁴(95-digit number)

25651843881179841603…86242222013882820319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.565 × 10⁹⁴(95-digit number)

25651843881179841603…86242222013882820321

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

5.130 × 10⁹⁴(95-digit number)

51303687762359683206…72484444027765640639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.130 × 10⁹⁴(95-digit number)

51303687762359683206…72484444027765640641

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

1.026 × 10⁹⁵(96-digit number)

10260737552471936641…44968888055531281279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.026 × 10⁹⁵(96-digit number)

10260737552471936641…44968888055531281281

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