Block #441,822

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2014, 10:00:10 AM · Difficulty 10.3492 · 6,354,696 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70feea62d8deb27f1d093cc4361f6caa9ea055b9cfa2b5304797c5ddb796a5e5

View on Chainz ↗

Height

#441,822

Difficulty

10.349189

Transactions

Size

2.36 KB

Version

Bits

0a596477

Nonce

10,116

Timestamp

3/13/2014, 10:00:10 AM

Confirmations

6,354,696

Mined by

⛏️ aS!AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

7ae2ad4bdd4d543d7998558724733770661a8353e2a9307943d5d16e862f58c3

Transactions (2)

Coinbased077c6de69a864…42dc609d8b2f3d

1 in → 24 out9.3200 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

16e12608e8748f…402c33d3c81b33

12 in → 1 out315.6190 XPM1.41 KB

AcBhg3ZT…yDiF6BoG

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.

3.953 × 10⁹⁴(95-digit number)

39531212047291471362…71199401303733701199

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

3.953 × 10⁹⁴(95-digit number)

39531212047291471362…71199401303733701199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.953 × 10⁹⁴(95-digit number)

39531212047291471362…71199401303733701201

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

7.906 × 10⁹⁴(95-digit number)

79062424094582942725…42398802607467402399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.906 × 10⁹⁴(95-digit number)

79062424094582942725…42398802607467402401

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

1.581 × 10⁹⁵(96-digit number)

15812484818916588545…84797605214934804799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.581 × 10⁹⁵(96-digit number)

15812484818916588545…84797605214934804801

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

3.162 × 10⁹⁵(96-digit number)

31624969637833177090…69595210429869609599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.162 × 10⁹⁵(96-digit number)

31624969637833177090…69595210429869609601

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

6.324 × 10⁹⁵(96-digit number)

63249939275666354180…39190420859739219199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.324 × 10⁹⁵(96-digit number)

63249939275666354180…39190420859739219201

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