Block #189,593

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/1/2013, 10:07:37 PM · Difficulty 9.8733 · 6,619,563 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c85708f38daee2addfadac831eb8cfd76bfb2f1e51e13ac3f1eab7566e6272df

View on Chainz ↗

Height

#189,593

Difficulty

9.873305

Transactions

Size

1.15 KB

Version

Bits

09df90f0

Nonce

41,524

Timestamp

10/1/2013, 10:07:37 PM

Confirmations

6,619,563

Mined by

⛏️ P2SHAHnBbSZUB33VknNc1hSqs87dGJRVfat6WW

Merkle Root

7f28b3656a11770d8cce40468c01c725fddd9581a8099dd181e775361b6af57a

Transactions (4)

Coinbase6945349333a6ee…6c1c89d4fd9886

1 in → 1 out10.2700 XPM109 B

AHnBbSZU…RVfat6WW

7c6fbbcb81609c…7593563a1af2a8

3 in → 2 out17.0364 XPM523 B

ATjhsNrx…SWUj9KSd AUUJC7ne…cmZaPWM6

0880671d5e092b…bac4bb0014f194

1 in → 2 out100.2569 XPM227 B

AHfxxirc…3zz2AL3r AKYAiFmn…e8LhWRDr

d1c7a0fa85c4f5…44247c7fe681d0

1 in → 2 out2.6318 XPM226 B

Advx4gtY…xTnCF9wq AdYCrGfc…q1Xrj1Ev

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.

3.911 × 10⁹⁴(95-digit number)

39116391061480106206…89559007930125857279

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

3.911 × 10⁹⁴(95-digit number)

39116391061480106206…89559007930125857279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.911 × 10⁹⁴(95-digit number)

39116391061480106206…89559007930125857281

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

7.823 × 10⁹⁴(95-digit number)

78232782122960212412…79118015860251714559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.823 × 10⁹⁴(95-digit number)

78232782122960212412…79118015860251714561

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

1.564 × 10⁹⁵(96-digit number)

15646556424592042482…58236031720503429119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.564 × 10⁹⁵(96-digit number)

15646556424592042482…58236031720503429121

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

3.129 × 10⁹⁵(96-digit number)

31293112849184084965…16472063441006858239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.129 × 10⁹⁵(96-digit number)

31293112849184084965…16472063441006858241

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

6.258 × 10⁹⁵(96-digit number)

62586225698368169930…32944126882013716479

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 #189,593

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