Block #2,267,119

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/25/2017, 9:38:53 AM · Difficulty 10.9516 · 4,566,841 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f898f61a477975463afff15be344898602856041b966687070fb82d0b2128a68

View on Chainz ↗

Height

#2,267,119

Difficulty

10.951590

Transactions

Size

1.14 KB

Version

Bits

0af39b61

Nonce

568,321,401

Timestamp

8/25/2017, 9:38:53 AM

Confirmations

4,566,841

Mined by

⛏️ P2SHASHod48sstKMcN53wM65rxiJtELjSnRFfA

Merkle Root

f705df3edc6fc2f38b5616d3618510e8bc5a4e0f3d354ef0db007d48e0fe7883

Transactions (2)

Coinbased10ff346fbcad6…a7a96134f8b4b6

1 in → 1 out8.3300 XPM110 B

ASHod48s…LjSnRFfA

0913e109e2f0ec…0d2f7eee04f6b0

6 in → 2 out1910.0996 XPM965 B

APCLwsZN…Y9nxkbdb Aa6r34eK…xxsSat5o

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.

6.296 × 10⁹⁴(95-digit number)

62966771144033635643…53148663971828193279

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

6.296 × 10⁹⁴(95-digit number)

62966771144033635643…53148663971828193279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.296 × 10⁹⁴(95-digit number)

62966771144033635643…53148663971828193281

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

1.259 × 10⁹⁵(96-digit number)

12593354228806727128…06297327943656386559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.259 × 10⁹⁵(96-digit number)

12593354228806727128…06297327943656386561

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

2.518 × 10⁹⁵(96-digit number)

25186708457613454257…12594655887312773119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.518 × 10⁹⁵(96-digit number)

25186708457613454257…12594655887312773121

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

5.037 × 10⁹⁵(96-digit number)

50373416915226908515…25189311774625546239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.037 × 10⁹⁵(96-digit number)

50373416915226908515…25189311774625546241

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

1.007 × 10⁹⁶(97-digit number)

10074683383045381703…50378623549251092479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.007 × 10⁹⁶(97-digit number)

10074683383045381703…50378623549251092481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.014 × 10⁹⁶(97-digit number)

20149366766090763406…00757247098502184959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,267,119

Cookie Preferences