Block #440,176

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 6:19:02 AM · Difficulty 10.3503 · 6,355,745 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b59a17ef40f104cdf97ac8441b58821c882a753d0c55e15b124b13875f2eea28

View on Chainz ↗

Height

#440,176

Difficulty

10.350314

Transactions

Size

2.23 KB

Version

Bits

0a59ae30

Nonce

38,246

Timestamp

3/12/2014, 6:19:02 AM

Confirmations

6,355,745

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

50dd3c7bf34bb15ac3d3046bf050ad2a18a5814a62455894cb7f6aa7e578c2b4

Transactions (3)

Coinbase46e72536949bbc…01ea3cf1f3ff02

1 in → 1 out9.3600 XPM110 B

AeKNrjNj…1NEq95Ta

f0a1f65d39ce70…9ebdeda8dc64db

5 in → 2 out15.0800 XPM816 B

AVBZzS2Y…R8jhKBN4 ARjCZoxd…CwTLbpGc

a357ee855a1da5…c63711f5b0a04b

8 in → 2 out17.8370 XPM1.23 KB

AVBZzS2Y…R8jhKBN4 AZ7qtcbR…TyRE8rPn

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.

7.636 × 10⁹⁶(97-digit number)

76366912654848990590…49619456669581174239

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

7.636 × 10⁹⁶(97-digit number)

76366912654848990590…49619456669581174239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.636 × 10⁹⁶(97-digit number)

76366912654848990590…49619456669581174241

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

1.527 × 10⁹⁷(98-digit number)

15273382530969798118…99238913339162348479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.527 × 10⁹⁷(98-digit number)

15273382530969798118…99238913339162348481

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

3.054 × 10⁹⁷(98-digit number)

30546765061939596236…98477826678324696959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.054 × 10⁹⁷(98-digit number)

30546765061939596236…98477826678324696961

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

6.109 × 10⁹⁷(98-digit number)

61093530123879192472…96955653356649393919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.109 × 10⁹⁷(98-digit number)

61093530123879192472…96955653356649393921

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

1.221 × 10⁹⁸(99-digit number)

12218706024775838494…93911306713298787839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.221 × 10⁹⁸(99-digit number)

12218706024775838494…93911306713298787841

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