Block #444,162

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 2:07:12 AM · Difficulty 10.3431 · 6,362,678 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65a29f5eeb67430743c6f22100d57d3577474eed2bbc8ac3f527cc4496076d3f

View on Chainz ↗

Height

#444,162

Difficulty

10.343055

Transactions

Size

6.64 KB

Version

Bits

0a57d27c

Nonce

530,404

Timestamp

3/15/2014, 2:07:12 AM

Confirmations

6,362,678

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

6ce1710ebe83d0891a78a3370eefca41689482cae2110db341cf46e28b36b9a4

Transactions (3)

Coinbase3c78b41059a671…8dc6594aa354ab

1 in → 1 out9.4000 XPM110 B

AeKNrjNj…1NEq95Ta

5bef9e83ffb622…3a0fb997015227

42 in → 2 out139.2105 XPM5.69 KB

AX7gbCES…HCFkaYNg AR24vtgA…DNdtqa6z

86f63fab5a693f…02da5082db9f7b

4 in → 7 out19.3623 XPM772 B

AVb4Tt4v…3Ze2LZ5q APiJPPBV…oMd88xJd AK3vz3dH…9NvorskL AVBgdTW6…6N4QfJBJ AHrFNmf8…hpqU2WtU

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.

2.333 × 10⁹⁸(99-digit number)

23338241241417350507…55772649967183001269

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

2.333 × 10⁹⁸(99-digit number)

23338241241417350507…55772649967183001269

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.333 × 10⁹⁸(99-digit number)

23338241241417350507…55772649967183001271

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

4.667 × 10⁹⁸(99-digit number)

46676482482834701014…11545299934366002539

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.667 × 10⁹⁸(99-digit number)

46676482482834701014…11545299934366002541

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

9.335 × 10⁹⁸(99-digit number)

93352964965669402029…23090599868732005079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.335 × 10⁹⁸(99-digit number)

93352964965669402029…23090599868732005081

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

1.867 × 10⁹⁹(100-digit number)

18670592993133880405…46181199737464010159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.867 × 10⁹⁹(100-digit number)

18670592993133880405…46181199737464010161

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

3.734 × 10⁹⁹(100-digit number)

37341185986267760811…92362399474928020319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.734 × 10⁹⁹(100-digit number)

37341185986267760811…92362399474928020321

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 #444,162

Cookie Preferences