Block #325,166

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/22/2013, 8:19:21 PM · Difficulty 10.2076 · 6,488,737 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8417fed8f0113ba655daecea051b436ae7a37fa5a4994cad0d487c7659e8d7a7

View on Chainz ↗

Height

#325,166

Difficulty

10.207557

Transactions

Size

1.01 KB

Version

Bits

0a35227a

Nonce

5,703

Timestamp

12/22/2013, 8:19:21 PM

Confirmations

6,488,737

Mined by

⛏️ .aRI&AQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

02142d1699e3479de9a8b9182f6228b34794f2db5ee64724385d95dce86ec7e5

Transactions (1)

Coinbase02142d1699e347…5d95dce86ec7e5

1 in → 26 out9.5800 XPM947 B

AQwRN8bE…V8PsTcY9 AQ8QAT3J…rCFKuVbR Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AG5YAjec…VhA4Aeh1

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.

2.650 × 10⁹⁴(95-digit number)

26507756529662855620…39531061027038959319

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

2.650 × 10⁹⁴(95-digit number)

26507756529662855620…39531061027038959319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.650 × 10⁹⁴(95-digit number)

26507756529662855620…39531061027038959321

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

5.301 × 10⁹⁴(95-digit number)

53015513059325711240…79062122054077918639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.301 × 10⁹⁴(95-digit number)

53015513059325711240…79062122054077918641

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

1.060 × 10⁹⁵(96-digit number)

10603102611865142248…58124244108155837279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.060 × 10⁹⁵(96-digit number)

10603102611865142248…58124244108155837281

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

2.120 × 10⁹⁵(96-digit number)

21206205223730284496…16248488216311674559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.120 × 10⁹⁵(96-digit number)

21206205223730284496…16248488216311674561

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

4.241 × 10⁹⁵(96-digit number)

42412410447460568992…32496976432623349119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.241 × 10⁹⁵(96-digit number)

42412410447460568992…32496976432623349121

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 #325,166

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