Block #182,975

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/27/2013, 4:55:18 PM · Difficulty 9.8577 · 6,625,056 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

774d16633e84f3c53b5ab0b99ee448a2c4bf8c4214817af6b958b8691fe7e978

View on Chainz ↗

Height

#182,975

Difficulty

9.857713

Transactions

Size

1019 B

Version

Bits

09db930e

Nonce

6,323

Timestamp

9/27/2013, 4:55:18 PM

Confirmations

6,625,056

Mined by

⛏️ P2SHAXtUHczob3NNdpiGvxAE1JUJfgKe72YFw4

Merkle Root

bb5b21ac57e049694367388ec905d657d76dab1d1a9a1526812ea11948329889

Transactions (2)

Coinbase2882a8e6fef0ad…a6fca6af0ec29a

1 in → 1 out10.2900 XPM110 B

AXtUHczo…Ke72YFw4

ff95450e8f34ce…cc7da27ec86aee

5 in → 2 out10.7438 XPM819 B

AXpUmx99…rjJpdn1S AQJS4weN…EFri8a5Q

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.

1.047 × 10⁹⁴(95-digit number)

10474865216876050908…61314753239161820759

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

1.047 × 10⁹⁴(95-digit number)

10474865216876050908…61314753239161820759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.047 × 10⁹⁴(95-digit number)

10474865216876050908…61314753239161820761

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

2.094 × 10⁹⁴(95-digit number)

20949730433752101817…22629506478323641519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.094 × 10⁹⁴(95-digit number)

20949730433752101817…22629506478323641521

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

4.189 × 10⁹⁴(95-digit number)

41899460867504203634…45259012956647283039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.189 × 10⁹⁴(95-digit number)

41899460867504203634…45259012956647283041

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

8.379 × 10⁹⁴(95-digit number)

83798921735008407268…90518025913294566079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.379 × 10⁹⁴(95-digit number)

83798921735008407268…90518025913294566081

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

1.675 × 10⁹⁵(96-digit number)

16759784347001681453…81036051826589132159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #182,975

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