Block #189,225

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/1/2013, 4:40:58 PM · Difficulty 9.8724 · 6,618,689 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a67956aa875726e5d6be7484b93203765c9d80233ee875230aa4873e12b48601

View on Chainz ↗

Height

#189,225

Difficulty

9.872353

Transactions

Size

1016 B

Version

Bits

09df5288

Nonce

465,498

Timestamp

10/1/2013, 4:40:58 PM

Confirmations

6,618,689

Mined by

⛏️ P2SHARUhEWzBvtBer1aUWrxs7fq5tpUtu9Rxw3

Merkle Root

ecd779795ab9780ec470318e58995828b3bbebb756dc70ee16461811e5dce753

Transactions (2)

Coinbase5d2c0b758d9ce9…bea927948b2b67

1 in → 1 out10.2600 XPM109 B

ARUhEWzB…Utu9Rxw3

2dbbe1709254d1…c0394fc20cae36

5 in → 2 out10.0233 XPM817 B

AS8XmsKo…KSPsgeBR ARjJVbsL…5WFWCLob

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.

3.777 × 10⁹⁵(96-digit number)

37777556347290807920…71351455708996123839

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

3.777 × 10⁹⁵(96-digit number)

37777556347290807920…71351455708996123839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.777 × 10⁹⁵(96-digit number)

37777556347290807920…71351455708996123841

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

7.555 × 10⁹⁵(96-digit number)

75555112694581615841…42702911417992247679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.555 × 10⁹⁵(96-digit number)

75555112694581615841…42702911417992247681

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

1.511 × 10⁹⁶(97-digit number)

15111022538916323168…85405822835984495359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.511 × 10⁹⁶(97-digit number)

15111022538916323168…85405822835984495361

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

3.022 × 10⁹⁶(97-digit number)

30222045077832646336…70811645671968990719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.022 × 10⁹⁶(97-digit number)

30222045077832646336…70811645671968990721

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

6.044 × 10⁹⁶(97-digit number)

60444090155665292672…41623291343937981439

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 #189,225

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