Block #2,266,078

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/24/2017, 4:32:13 PM · Difficulty 10.9514 · 4,575,224 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ae602e54c03172cac0a2d29d17a7080f9c8c057ba87cc7dc09f67de4a1892db

View on Chainz ↗

Height

#2,266,078

Difficulty

10.951421

Transactions

Size

1.72 KB

Version

Bits

0af39053

Nonce

442,742,541

Timestamp

8/24/2017, 4:32:13 PM

Confirmations

4,575,224

Mined by

⛏️ P2SHAegCLf8dAK4V4JTXTUzFhsRNojBhZXhKYF

Merkle Root

1d3f1c0495724971dd9c24f17af98d419b00a829bec8129d9f8c4f2e303545c5

Transactions (2)

Coinbase13f810b2d27673…b279381ad3651b

1 in → 1 out8.3400 XPM110 B

AegCLf8d…BhZXhKYF

16e89552170cab…10381cfe4edbe0

10 in → 2 out2873.4511 XPM1.52 KB

AJdomnpT…wsZKT4Nd AKXwgFFC…37apXMyJ

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.

7.057 × 10⁹⁵(96-digit number)

70574927794278930302…67863696516855002879

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

7.057 × 10⁹⁵(96-digit number)

70574927794278930302…67863696516855002879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.057 × 10⁹⁵(96-digit number)

70574927794278930302…67863696516855002881

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

1.411 × 10⁹⁶(97-digit number)

14114985558855786060…35727393033710005759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.411 × 10⁹⁶(97-digit number)

14114985558855786060…35727393033710005761

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

2.822 × 10⁹⁶(97-digit number)

28229971117711572121…71454786067420011519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.822 × 10⁹⁶(97-digit number)

28229971117711572121…71454786067420011521

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

5.645 × 10⁹⁶(97-digit number)

56459942235423144242…42909572134840023039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.645 × 10⁹⁶(97-digit number)

56459942235423144242…42909572134840023041

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

1.129 × 10⁹⁷(98-digit number)

11291988447084628848…85819144269680046079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.129 × 10⁹⁷(98-digit number)

11291988447084628848…85819144269680046081

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 #2,266,078

Cookie Preferences