Block #420,056

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/26/2014, 3:44:11 AM · Difficulty 10.3655 · 6,378,506 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d5934b8443d3bb2e6011afc52c4406edee636cdcd2c6145ffb116ed8ccd3edc3

View on Chainz ↗

Height

#420,056

Difficulty

10.365489

Transactions

Size

1002 B

Version

Bits

0a5d90b7

Nonce

98,341

Timestamp

2/26/2014, 3:44:11 AM

Confirmations

6,378,506

Mined by

⛏️ haSAZV4TwxQjib54Zzk9TCxNRouXM8JnQqSoH

Merkle Root

9c2e9b54068a1077e4123ead2a38187816d065994e656b2fb980b210793d40d4

Transactions (1)

Coinbase9c2e9b54068a10…80b210793d40d4

1 in → 25 out9.2900 XPM913 B

AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn ATKK7iFz…wZm46KN1

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.

1.438 × 10⁹³(94-digit number)

14387252827401797392…13902284248047508309

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

1.438 × 10⁹³(94-digit number)

14387252827401797392…13902284248047508309

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.438 × 10⁹³(94-digit number)

14387252827401797392…13902284248047508311

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

2.877 × 10⁹³(94-digit number)

28774505654803594785…27804568496095016619

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.877 × 10⁹³(94-digit number)

28774505654803594785…27804568496095016621

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

5.754 × 10⁹³(94-digit number)

57549011309607189571…55609136992190033239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.754 × 10⁹³(94-digit number)

57549011309607189571…55609136992190033241

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

1.150 × 10⁹⁴(95-digit number)

11509802261921437914…11218273984380066479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.150 × 10⁹⁴(95-digit number)

11509802261921437914…11218273984380066481

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

2.301 × 10⁹⁴(95-digit number)

23019604523842875828…22436547968760132959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.301 × 10⁹⁴(95-digit number)

23019604523842875828…22436547968760132961

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