Block #418,763

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 3:28:34 AM · Difficulty 10.3839 · 6,397,634 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c67268bde5eb6f770087beb2a20bd6863ec9c366eb967b226272a30a977c0689

View on Chainz ↗

Height

#418,763

Difficulty

10.383856

Transactions

Size

659 B

Version

Bits

0a62445b

Nonce

221,469

Timestamp

2/25/2014, 3:28:34 AM

Confirmations

6,397,634

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7d16bcc31e57c92b11b43328d9357b2d87f47521a7078ca1284e18b1612bfc2d

Transactions (3)

Coinbasec31f988d6b38e7…ac30aff99d2684

1 in → 1 out9.2800 XPM116 B

AbwWkWZt…kawDhufa

9798eaafa5dc4b…c63e9f3306ae54

1 in → 2 out3.8248 XPM226 B

Ac1bSd2Z…YVgkWmcf AXnL68UR…jsxeGUhN

89f4ace2630c5d…7ab0d9d94d2911

1 in → 2 out4.3288 XPM226 B

AMiVTMtt…4Knq1ve9 AM4x8Atf…S36u6zKo

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.

6.074 × 10⁹⁶(97-digit number)

60744126315694183270…22757921879435710639

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

6.074 × 10⁹⁶(97-digit number)

60744126315694183270…22757921879435710639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.074 × 10⁹⁶(97-digit number)

60744126315694183270…22757921879435710641

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

1.214 × 10⁹⁷(98-digit number)

12148825263138836654…45515843758871421279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.214 × 10⁹⁷(98-digit number)

12148825263138836654…45515843758871421281

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

2.429 × 10⁹⁷(98-digit number)

24297650526277673308…91031687517742842559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.429 × 10⁹⁷(98-digit number)

24297650526277673308…91031687517742842561

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

4.859 × 10⁹⁷(98-digit number)

48595301052555346616…82063375035485685119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.859 × 10⁹⁷(98-digit number)

48595301052555346616…82063375035485685121

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

9.719 × 10⁹⁷(98-digit number)

97190602105110693233…64126750070971370239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.719 × 10⁹⁷(98-digit number)

97190602105110693233…64126750070971370241

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 #418,763

Cookie Preferences