Block #193,251

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 9:59:52 AM · Difficulty 9.8758 · 6,616,822 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ad60b5dba6af9d3fbc9e083c5b19d6f5703c87e961746d5d51d8b6e25965c4ae

View on Chainz ↗

Height

#193,251

Difficulty

9.875819

Transactions

Size

3.00 KB

Version

Bits

09e035a9

Nonce

1,164,885,994

Timestamp

10/4/2013, 9:59:52 AM

Confirmations

6,616,822

Mined by

⛏️ RNAakGxn9Jc4yzByFeTeovZhRe7xd7mTfZVK

Merkle Root

3ca889b02a43d053c75f0079352477b6a7c4aac6356a8c06bae93b64c8b449dc

Transactions (1)

Coinbase3ca889b02a43d0…e93b64c8b449dc

1 in → 86 out10.2100 XPM2.92 KB

AakGxn9J…d7mTfZVK AcKcNjCB…MZipfo4V ANAVEjQm…6wqP126u APRCUQcB…mVjD4Jx1 AR1jhzXB…TNHNWyCm

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.

1.270 × 10⁹³(94-digit number)

12709195391044308651…84675631012770653439

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

1.270 × 10⁹³(94-digit number)

12709195391044308651…84675631012770653439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.270 × 10⁹³(94-digit number)

12709195391044308651…84675631012770653441

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

2.541 × 10⁹³(94-digit number)

25418390782088617303…69351262025541306879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.541 × 10⁹³(94-digit number)

25418390782088617303…69351262025541306881

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

5.083 × 10⁹³(94-digit number)

50836781564177234607…38702524051082613759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.083 × 10⁹³(94-digit number)

50836781564177234607…38702524051082613761

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

1.016 × 10⁹⁴(95-digit number)

10167356312835446921…77405048102165227519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.016 × 10⁹⁴(95-digit number)

10167356312835446921…77405048102165227521

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

2.033 × 10⁹⁴(95-digit number)

20334712625670893842…54810096204330455039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.033 × 10⁹⁴(95-digit number)

20334712625670893842…54810096204330455041

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 #193,251

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