Block #406,405

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/16/2014, 6:04:15 AM · Difficulty 10.4306 · 6,396,907 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3dd1336233aa61cf754a74ceba6da4f6d8eff49aa40ed79582f1d5555b8ed21c

View on Chainz ↗

Height

#406,405

Difficulty

10.430579

Transactions

Size

868 B

Version

Bits

0a6e3a66

Nonce

91,292

Timestamp

2/16/2014, 6:04:15 AM

Confirmations

6,396,907

Mined by

⛏️ 3aSTAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

8c0fae086763b6f883e4a7c506af4db6e6b321c9e76b6e0c7f9baeed95c9c10e

Transactions (1)

Coinbase8c0fae086763b6…9baeed95c9c10e

1 in → 21 out9.1800 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AYtDvcGs…VuAcA7m7

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.

7.277 × 10⁹⁷(98-digit number)

72770618471370500542…56388385947448350089

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

7.277 × 10⁹⁷(98-digit number)

72770618471370500542…56388385947448350089

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.277 × 10⁹⁷(98-digit number)

72770618471370500542…56388385947448350091

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

1.455 × 10⁹⁸(99-digit number)

14554123694274100108…12776771894896700179

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.455 × 10⁹⁸(99-digit number)

14554123694274100108…12776771894896700181

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

2.910 × 10⁹⁸(99-digit number)

29108247388548200216…25553543789793400359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.910 × 10⁹⁸(99-digit number)

29108247388548200216…25553543789793400361

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

5.821 × 10⁹⁸(99-digit number)

58216494777096400433…51107087579586800719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.821 × 10⁹⁸(99-digit number)

58216494777096400433…51107087579586800721

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

1.164 × 10⁹⁹(100-digit number)

11643298955419280086…02214175159173601439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.164 × 10⁹⁹(100-digit number)

11643298955419280086…02214175159173601441

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