Block #1,182,174

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/4/2015, 3:38:13 AM · Difficulty 10.9146 · 5,660,104 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e7645045b9c1a7db5b9ee76aa2890cb99cefdae21fce860cba638d8289ec55b

View on Chainz ↗

Height

#1,182,174

Difficulty

10.914622

Transactions

Size

427 B

Version

Bits

0aea24b1

Nonce

245,826,571

Timestamp

8/4/2015, 3:38:13 AM

Confirmations

5,660,104

Mined by

⛏️ P2SHAcK72XbQqBxVH1q95e3C2hhMHNDgVzBRVE

Merkle Root

f8747e02773b660e9bd7b9ae4fd820ed3fa676772d134528db852f05b87fc73e

Transactions (2)

Coinbase4447ebfb001dbe…6c2a20f9baaeb9

1 in → 1 out8.3900 XPM110 B

AcK72XbQ…DgVzBRVE

a3efec4cec0137…8c7db9671f320e

1 in → 2 out3.7089 XPM226 B

AcuM7XiJ…5uND8Jce ALngzm1P…Qb1UAePe

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.

1.396 × 10⁹⁸(99-digit number)

13962996608515829717…17860090616364400639

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

1.396 × 10⁹⁸(99-digit number)

13962996608515829717…17860090616364400639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.396 × 10⁹⁸(99-digit number)

13962996608515829717…17860090616364400641

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

2.792 × 10⁹⁸(99-digit number)

27925993217031659434…35720181232728801279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.792 × 10⁹⁸(99-digit number)

27925993217031659434…35720181232728801281

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

5.585 × 10⁹⁸(99-digit number)

55851986434063318869…71440362465457602559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.585 × 10⁹⁸(99-digit number)

55851986434063318869…71440362465457602561

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

1.117 × 10⁹⁹(100-digit number)

11170397286812663773…42880724930915205119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.117 × 10⁹⁹(100-digit number)

11170397286812663773…42880724930915205121

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

2.234 × 10⁹⁹(100-digit number)

22340794573625327547…85761449861830410239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.234 × 10⁹⁹(100-digit number)

22340794573625327547…85761449861830410241

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 #1,182,174

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