Block #192,777

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 2:27:15 AM · Difficulty 9.8750 · 6,603,128 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e06660ac1f85cd1c1f87fc72aba593d64243559d88ba1ae27580af663d4123f0

View on Chainz ↗

Height

#192,777

Difficulty

9.875044

Transactions

Size

4.10 KB

Version

Bits

09e002e7

Nonce

1,164,856,460

Timestamp

10/4/2013, 2:27:15 AM

Confirmations

6,603,128

Mined by

⛏️ RN'UAVp5teGiHw1YKkP5E1aka54stN6zMrJdp7

Merkle Root

dcf365f9801e81b7b2fa2e8f79d3702fe78eef1678c4c92cc84776a350cc490e

Transactions (1)

Coinbasedcf365f9801e81…4776a350cc490e

1 in → 119 out10.1900 XPM4.01 KB

AVp5teGi…6zMrJdp7 AXAzNior…1Vi1qRfY APLg1hys…r5atPnTe AKeDh1uS…Th9Hwfjg AKF2rJVd…fNsDgS32

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.

3.794 × 10⁹⁸(99-digit number)

37943842703214027923…11645151892391155839

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

3.794 × 10⁹⁸(99-digit number)

37943842703214027923…11645151892391155839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.794 × 10⁹⁸(99-digit number)

37943842703214027923…11645151892391155841

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

7.588 × 10⁹⁸(99-digit number)

75887685406428055847…23290303784782311679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.588 × 10⁹⁸(99-digit number)

75887685406428055847…23290303784782311681

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

1.517 × 10⁹⁹(100-digit number)

15177537081285611169…46580607569564623359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.517 × 10⁹⁹(100-digit number)

15177537081285611169…46580607569564623361

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

3.035 × 10⁹⁹(100-digit number)

30355074162571222339…93161215139129246719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.035 × 10⁹⁹(100-digit number)

30355074162571222339…93161215139129246721

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

6.071 × 10⁹⁹(100-digit number)

60710148325142444678…86322430278258493439

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