Block #173,785

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/21/2013, 6:09:31 AM · Difficulty 9.8598 · 6,667,994 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2f382f156354174301bc47731bfd11749fdcc3fa8f8cdb295502dee19eb7ba8d

View on Chainz ↗

Height

#173,785

Difficulty

9.859839

Transactions

Size

5.72 KB

Version

Bits

09dc1e67

Nonce

464,493

Timestamp

9/21/2013, 6:09:31 AM

Confirmations

6,667,994

Mined by

⛏️ P2SHATK4r8GhoVczEZqtspX4UTeEK5Usic4A9N

Merkle Root

931469dfe8ee186bb9ce330d61a938d8be9fde4599734a4386872e104dde0cd9

Transactions (2)

Coinbase92e9102703c57d…17a6ffee4f2421

1 in → 1 out10.3300 XPM109 B

ATK4r8Gh…Usic4A9N

3186dd4b938f3c…6a1b486707e497

49 in → 2 out502.7233 XPM5.53 KB

AVi8vvsy…xEdCzX8H AL3jCG2K…moye79K3

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.

1.037 × 10⁹¹(92-digit number)

10377405650231583667…05702718079192196399

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

1.037 × 10⁹¹(92-digit number)

10377405650231583667…05702718079192196399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.037 × 10⁹¹(92-digit number)

10377405650231583667…05702718079192196401

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

2.075 × 10⁹¹(92-digit number)

20754811300463167334…11405436158384392799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.075 × 10⁹¹(92-digit number)

20754811300463167334…11405436158384392801

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

4.150 × 10⁹¹(92-digit number)

41509622600926334668…22810872316768785599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.150 × 10⁹¹(92-digit number)

41509622600926334668…22810872316768785601

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

8.301 × 10⁹¹(92-digit number)

83019245201852669336…45621744633537571199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.301 × 10⁹¹(92-digit number)

83019245201852669336…45621744633537571201

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

1.660 × 10⁹²(93-digit number)

16603849040370533867…91243489267075142399

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 #173,785

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