Block #193,371

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 11:36:18 AM · Difficulty 9.8762 · 6,610,942 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41ae23225a664abaea559675161c79a1ba9475c07fee3544a582a8487d538ebf

View on Chainz ↗

Height

#193,371

Difficulty

9.876233

Transactions

Size

1.96 KB

Version

Bits

09e050c7

Nonce

60,599

Timestamp

10/4/2013, 11:36:18 AM

Confirmations

6,610,942

Mined by

⛏️ P2SHAbGkvdxHZ4BVXfnK4PvSdcrNAUoihMdBXd

Merkle Root

81d45a8b9f09f4ed176d1a08a0fb22dfaf5f5468b7803fc1dabe478f86384c40

Transactions (5)

Coinbase4360b85daf79ba…0d72ed3d321206

1 in → 1 out10.2800 XPM100 B

AbGkvdxH…oihMdBXd

6c92ebfc9f2e54…a8f34e27ba7713

2 in → 6 out20.4800 XPM441 B

AFq51nP4…FqYfXapg AFvtfamp…AgWjuUgr ATn5gfzL…UWGXwTUs AcyPVp7N…dDULWcdA AGdYdg5f…ZrePPako

901cfc510b279d…46f123b9785bc4

1 in → 3 out10.2300 XPM225 B

AQXUSoBL…CzbjKp8b ANvtpRa1…QjsraDJz AUT1qxTx…t5B3qd8Z

25bf1c5cf1ad73…370960a8dcddc5

2 in → 6 out20.4800 XPM443 B

ANvtpRa1…QjsraDJz ANxERLYc…v7fC1vqc AQXUSoBL…CzbjKp8b AHADV2Ly…7mcKNDYV AVKfZvtY…sCa4NTcM

340367f003605e…0da177a7efd68e

4 in → 4 out12.3286 XPM704 B

AQXUSoBL…CzbjKp8b AKyT5sag…P1gmPYoR ALsqSwWV…uZ7sTz8x ANvtpRa1…QjsraDJz

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.

1.772 × 10⁹⁴(95-digit number)

17720949019923156451…80194264097475424399

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

1.772 × 10⁹⁴(95-digit number)

17720949019923156451…80194264097475424399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.772 × 10⁹⁴(95-digit number)

17720949019923156451…80194264097475424401

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

3.544 × 10⁹⁴(95-digit number)

35441898039846312902…60388528194950848799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.544 × 10⁹⁴(95-digit number)

35441898039846312902…60388528194950848801

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

7.088 × 10⁹⁴(95-digit number)

70883796079692625805…20777056389901697599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.088 × 10⁹⁴(95-digit number)

70883796079692625805…20777056389901697601

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

1.417 × 10⁹⁵(96-digit number)

14176759215938525161…41554112779803395199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.417 × 10⁹⁵(96-digit number)

14176759215938525161…41554112779803395201

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

2.835 × 10⁹⁵(96-digit number)

28353518431877050322…83108225559606790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.835 × 10⁹⁵(96-digit number)

28353518431877050322…83108225559606790401

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