Block #403,905

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/14/2014, 11:56:00 AM · Difficulty 10.4324 · 6,404,812 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8b00dbaee64b352bbfa1c661c224485f47d969a4a59690d7968bd8f5eaa584c5

View on Chainz ↗

Height

#403,905

Difficulty

10.432409

Transactions

Size

900 B

Version

Bits

0a6eb25f

Nonce

199,115

Timestamp

2/14/2014, 11:56:00 AM

Confirmations

6,404,812

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ebdc264c0f1e96531e9dacd1f077226e20546edda6cfd826fd1a8dbc03ff0719

Transactions (1)

Coinbaseebdc264c0f1e96…1a8dbc03ff0719

1 in → 22 out9.1700 XPM811 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 Aac9Hjdg…P4ktypc3 AYRvXuTr…CkbwFeLY ARck9uUe…jQe3uJMp

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.

3.222 × 10⁹²(93-digit number)

32224218353957658638…77529502619734565999

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

3.222 × 10⁹²(93-digit number)

32224218353957658638…77529502619734565999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.222 × 10⁹²(93-digit number)

32224218353957658638…77529502619734566001

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

6.444 × 10⁹²(93-digit number)

64448436707915317276…55059005239469131999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.444 × 10⁹²(93-digit number)

64448436707915317276…55059005239469132001

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

1.288 × 10⁹³(94-digit number)

12889687341583063455…10118010478938263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.288 × 10⁹³(94-digit number)

12889687341583063455…10118010478938264001

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

2.577 × 10⁹³(94-digit number)

25779374683166126910…20236020957876527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.577 × 10⁹³(94-digit number)

25779374683166126910…20236020957876528001

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

5.155 × 10⁹³(94-digit number)

51558749366332253821…40472041915753055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.155 × 10⁹³(94-digit number)

51558749366332253821…40472041915753056001

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 #403,905

Cookie Preferences