Block #189,269

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/1/2013, 5:13:22 PM · Difficulty 9.8727 · 6,618,744 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

08333a53ac193a1fabca253a04d908a4d651444c774ba4de8805c1beaef978e0

View on Chainz ↗

Height

#189,269

Difficulty

9.872668

Transactions

Size

615 B

Version

Bits

09df6732

Nonce

119,540

Timestamp

10/1/2013, 5:13:22 PM

Confirmations

6,618,744

Mined by

⛏️ P2SHAGAZ2wz6EeAUJiVP8kFKgTNx8T84mNH2V3

Merkle Root

c5707fcc29b3ba0f6bc9ca02d97ae539355bb2e4d85fa1dfdde8ee0695ed4c24

Transactions (3)

Coinbase77b68ca3be2dca…7325a1d1708649

1 in → 1 out10.2600 XPM109 B

AGAZ2wz6…84mNH2V3

cda02d761f83c6…d0b8d22ba328e9

1 in → 1 out391.7721 XPM193 B

AKsVwf65…ZSDBi7dW

594f9b1a4a8d08…1215418808e00d

1 in → 2 out8.1980 XPM225 B

AUJB7Qq7…LGJhBUA3 AUD2SBQn…SgzK4VBw

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.

7.813 × 10⁸⁸(89-digit number)

78132719668253378161…52660045991995486399

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

7.813 × 10⁸⁸(89-digit number)

78132719668253378161…52660045991995486399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.813 × 10⁸⁸(89-digit number)

78132719668253378161…52660045991995486401

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

1.562 × 10⁸⁹(90-digit number)

15626543933650675632…05320091983990972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.562 × 10⁸⁹(90-digit number)

15626543933650675632…05320091983990972801

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

3.125 × 10⁸⁹(90-digit number)

31253087867301351264…10640183967981945599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.125 × 10⁸⁹(90-digit number)

31253087867301351264…10640183967981945601

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

6.250 × 10⁸⁹(90-digit number)

62506175734602702528…21280367935963891199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.250 × 10⁸⁹(90-digit number)

62506175734602702528…21280367935963891201

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

1.250 × 10⁹⁰(91-digit number)

12501235146920540505…42560735871927782399

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 #189,269

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