Block #192,710

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 1:37:48 AM · Difficulty 9.8746 · 6,597,124 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91b3af84cb5282a1b78534bc3f59e59b170d0dd226576147e510cd6d40b72db3

View on Chainz ↗

Height

#192,710

Difficulty

9.874632

Transactions

Size

3.91 KB

Version

Bits

09dfe7e2

Nonce

76,544

Timestamp

10/4/2013, 1:37:48 AM

Confirmations

6,597,124

Merkle Root

dda9ee0057a97af7d6c15a0b2bf77800475fe97b15ad366ad3589e8da32cf47e

Transactions (2)

Coinbase062dc5215b5f74…379e1f1a8b063f

1 in → 1 out10.2800 XPM109 B

Ad7RSx8z…nqAeF5cV

5a11d8071d6668…1104f61b30c6c1

30 in → 2 out306.6873 XPM3.72 KB

AWKpUf5f…S2RLN5dS AT3dRckg…iggfceho

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.

7.686 × 10⁹¹(92-digit number)

76865254942039172914…79216661348937305339

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

7.686 × 10⁹¹(92-digit number)

76865254942039172914…79216661348937305339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.686 × 10⁹¹(92-digit number)

76865254942039172914…79216661348937305341

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

1.537 × 10⁹²(93-digit number)

15373050988407834582…58433322697874610679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.537 × 10⁹²(93-digit number)

15373050988407834582…58433322697874610681

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

3.074 × 10⁹²(93-digit number)

30746101976815669165…16866645395749221359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.074 × 10⁹²(93-digit number)

30746101976815669165…16866645395749221361

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

6.149 × 10⁹²(93-digit number)

61492203953631338331…33733290791498442719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.149 × 10⁹²(93-digit number)

61492203953631338331…33733290791498442721

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

1.229 × 10⁹³(94-digit number)

12298440790726267666…67466581582996885439

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