Block #192,036

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/3/2013, 2:12:08 PM · Difficulty 9.8748 · 6,600,601 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b33cbea1f77e2e175c5d2af304c51cfd3160c397248ad79b4b54334df5fe5e28

View on Chainz ↗

Height

#192,036

Difficulty

9.874823

Transactions

Size

1.08 KB

Version

Bits

09dff464

Nonce

84,951

Timestamp

10/3/2013, 2:12:08 PM

Confirmations

6,600,601

Merkle Root

9552b1d258d596c2b91df80c5e707d1b5c266773f9290a0d0eab1fc87d6f12b9

Transactions (3)

Coinbase0d906b7df4da4b…7c41fff6bd7daa

1 in → 1 out10.2600 XPM109 B

AK86yoZS…rqUgrJ1Z

521d5204137b8f…f5da860c691564

3 in → 2 out300.0108 XPM522 B

ARxmAxSn…R3khZFpw AP7TVtgh…rdTHj9sH

804b381e83ec9f…803bdc75628e15

3 in → 1 out30.8000 XPM388 B

AQ3pJJru…FAMSi23x

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.

1.687 × 10⁹⁴(95-digit number)

16870514699148238122…55856715690116194959

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

1.687 × 10⁹⁴(95-digit number)

16870514699148238122…55856715690116194959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.687 × 10⁹⁴(95-digit number)

16870514699148238122…55856715690116194961

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

3.374 × 10⁹⁴(95-digit number)

33741029398296476244…11713431380232389919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.374 × 10⁹⁴(95-digit number)

33741029398296476244…11713431380232389921

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

6.748 × 10⁹⁴(95-digit number)

67482058796592952489…23426862760464779839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.748 × 10⁹⁴(95-digit number)

67482058796592952489…23426862760464779841

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

1.349 × 10⁹⁵(96-digit number)

13496411759318590497…46853725520929559679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.349 × 10⁹⁵(96-digit number)

13496411759318590497…46853725520929559681

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

2.699 × 10⁹⁵(96-digit number)

26992823518637180995…93707451041859119359

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