Block #212,369

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/16/2013, 6:07:48 AM · Difficulty 9.9188 · 6,598,435 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9cc55873c5a525309fbead05755483c0e18bee9aa73ee0beb6121870372c5b4a

View on Chainz ↗

Height

#212,369

Difficulty

9.918770

Transactions

Size

5.13 KB

Version

Bits

09eb3481

Nonce

1,164,766,467

Timestamp

10/16/2013, 6:07:48 AM

Confirmations

6,598,435

Mined by

⛏️ =R^-<AKUmXTVjkcUqYgzuHZ2Puq8PWXPfwi4Ebx

Merkle Root

d7a3975849239aabf5ec6778df6bd366b2667341c1caefe1d04d4a457b75d8ce

Transactions (1)

Coinbased7a3975849239a…4d4a457b75d8ce

1 in → 150 out10.0900 XPM5.04 KB

AKUmXTVj…Pfwi4Ebx AJWc12T9…gdZnUvYf Aau9Lf88…RBtXCd78 AcKcNjCB…MZipfo4V AHhf6UZe…1CwmCJdF

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.

6.124 × 10⁹¹(92-digit number)

61245699581973289289…31888114760967098799

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

6.124 × 10⁹¹(92-digit number)

61245699581973289289…31888114760967098799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.124 × 10⁹¹(92-digit number)

61245699581973289289…31888114760967098801

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

1.224 × 10⁹²(93-digit number)

12249139916394657857…63776229521934197599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.224 × 10⁹²(93-digit number)

12249139916394657857…63776229521934197601

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

2.449 × 10⁹²(93-digit number)

24498279832789315715…27552459043868395199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.449 × 10⁹²(93-digit number)

24498279832789315715…27552459043868395201

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

4.899 × 10⁹²(93-digit number)

48996559665578631431…55104918087736790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.899 × 10⁹²(93-digit number)

48996559665578631431…55104918087736790401

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

9.799 × 10⁹²(93-digit number)

97993119331157262862…10209836175473580799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.799 × 10⁹²(93-digit number)

97993119331157262862…10209836175473580801

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 #212,369

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