Block #133,189

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/25/2013, 9:35:33 AM · Difficulty 9.7920 · 6,677,811 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

03ef477abae72372ffa4322fb5b702c4e0bdbc019c37a9d31dd90281ff872f71

View on Chainz ↗

Height

#133,189

Difficulty

9.791999

Transactions

Size

806 B

Version

Bits

09cac073

Nonce

223

Timestamp

8/25/2013, 9:35:33 AM

Confirmations

6,677,811

Mined by

⛏️ P2SHAN4ze86k65bwKgcgz6ZhctgyMMkzTNsn4K

Merkle Root

9ccf42b9cb6dd42e74f8c576f665071184a2187df6f9343a8cfc7c7808c44758

Transactions (3)

Coinbasec7d0a564ace37e…acfc753a056b37

1 in → 1 out10.4300 XPM110 B

AN4ze86k…kzTNsn4K

41921f544bdcaf…8ae82da0e53bb5

1 in → 2 out1999.5700 XPM226 B

AH3C69ei…yj9SuS7P AcR3Kx2X…hcw1oGQP

4c0f2ce93e7fee…0ef7552d514781

2 in → 2 out3200.9900 XPM373 B

AH3C69ei…yj9SuS7P AN625exD…fcu6o3TB

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.

7.820 × 10¹¹⁰(111-digit number)

78205937995537181504…53903248640204618539

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

7.820 × 10¹¹⁰(111-digit number)

78205937995537181504…53903248640204618539

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.820 × 10¹¹⁰(111-digit number)

78205937995537181504…53903248640204618541

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

1.564 × 10¹¹¹(112-digit number)

15641187599107436300…07806497280409237079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.564 × 10¹¹¹(112-digit number)

15641187599107436300…07806497280409237081

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

3.128 × 10¹¹¹(112-digit number)

31282375198214872601…15612994560818474159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.128 × 10¹¹¹(112-digit number)

31282375198214872601…15612994560818474161

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

6.256 × 10¹¹¹(112-digit number)

62564750396429745203…31225989121636948319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.256 × 10¹¹¹(112-digit number)

62564750396429745203…31225989121636948321

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

1.251 × 10¹¹²(113-digit number)

12512950079285949040…62451978243273896639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.251 × 10¹¹²(113-digit number)

12512950079285949040…62451978243273896641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #133,189

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