Block #189,523

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/1/2013, 9:04:58 PM · Difficulty 9.8733 · 6,636,591 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

820d88bd41f499cf7fdf9f5e390dda2d3def37a64f3280224eacbab2dc43b99c

View on Chainz ↗

Height

#189,523

Difficulty

9.873254

Transactions

Size

721 B

Version

Bits

09df8d8c

Nonce

19,363

Timestamp

10/1/2013, 9:04:58 PM

Confirmations

6,636,591

Mined by

⛏️ P2SHAMMXU42qZ4UL7mggfRZGSeEy9V267DURSv

Merkle Root

910819dae335e3c5bfd0141bba5c7ce298fa4bdfc404977573a8dbf9294c20c4

Transactions (2)

Coinbase1fb4382e6d94aa…59057ec44e3727

1 in → 1 out10.2500 XPM109 B

AMMXU42q…267DURSv

063ca489b9d606…2169157a16de17

3 in → 2 out30.8000 XPM521 B

AVBmtpU9…kVLCmL6r AUNFudwi…yciB1G3d

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.

5.329 × 10⁹⁷(98-digit number)

53291757912420558246…41467074369162942719

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

5.329 × 10⁹⁷(98-digit number)

53291757912420558246…41467074369162942719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.329 × 10⁹⁷(98-digit number)

53291757912420558246…41467074369162942721

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

1.065 × 10⁹⁸(99-digit number)

10658351582484111649…82934148738325885439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.065 × 10⁹⁸(99-digit number)

10658351582484111649…82934148738325885441

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

2.131 × 10⁹⁸(99-digit number)

21316703164968223298…65868297476651770879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.131 × 10⁹⁸(99-digit number)

21316703164968223298…65868297476651770881

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

4.263 × 10⁹⁸(99-digit number)

42633406329936446597…31736594953303541759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.263 × 10⁹⁸(99-digit number)

42633406329936446597…31736594953303541761

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

8.526 × 10⁹⁸(99-digit number)

85266812659872893194…63473189906607083519

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 #189,523

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