Block #238,174

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/1/2013, 10:23:33 AM · Difficulty 9.9516 · 6,572,013 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dec7ad8cbda6256e0cac0f5fa5d536f296d2a0c7252d99c01a7eda740ebc9c51

View on Chainz ↗

Height

#238,174

Difficulty

9.951581

Transactions

Size

587 B

Version

Bits

09f39ad1

Nonce

8,811

Timestamp

11/1/2013, 10:23:33 AM

Confirmations

6,572,013

Mined by

⛏️ P2SHAQaCJsaU5a69V8Dtjoc2inAzh8MRLEgb1G

Merkle Root

ca013632e4ea208a232f0b970a0f5cd33e711aba9e728e13373177dd4ab24a4d

Transactions (2)

Coinbase9afad860a4f4a1…3f1cb521963464

1 in → 1 out10.0900 XPM109 B

AQaCJsaU…MRLEgb1G

63692f44c748c3…4c6ff7332f319d

3 in → 1 out30.4200 XPM387 B

AN7CTbAY…CXZXPsEU

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.

1.013 × 10⁹⁸(99-digit number)

10136207885826334340…58601080770215617279

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

1.013 × 10⁹⁸(99-digit number)

10136207885826334340…58601080770215617279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.013 × 10⁹⁸(99-digit number)

10136207885826334340…58601080770215617281

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

2.027 × 10⁹⁸(99-digit number)

20272415771652668680…17202161540431234559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.027 × 10⁹⁸(99-digit number)

20272415771652668680…17202161540431234561

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

4.054 × 10⁹⁸(99-digit number)

40544831543305337360…34404323080862469119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.054 × 10⁹⁸(99-digit number)

40544831543305337360…34404323080862469121

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

8.108 × 10⁹⁸(99-digit number)

81089663086610674720…68808646161724938239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.108 × 10⁹⁸(99-digit number)

81089663086610674720…68808646161724938241

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

1.621 × 10⁹⁹(100-digit number)

16217932617322134944…37617292323449876479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.621 × 10⁹⁹(100-digit number)

16217932617322134944…37617292323449876481

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 #238,174

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