Block #192,446

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/3/2013, 9:12:12 PM · Difficulty 9.8746 · 6,612,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b9da2c8cb0187007e93f10cddb64335d50c107efb39a1d85e4c01e54623dc6e2

View on Chainz ↗

Height

#192,446

Difficulty

9.874634

Transactions

Size

3.97 KB

Version

Bits

09dfe7fe

Nonce

1,164,809,359

Timestamp

10/3/2013, 9:12:12 PM

Confirmations

6,612,366

Mined by

⛏️ RMyASTyaa898M5NBF79EoWjK8Z3rSLKTnQv8K

Merkle Root

bf3c1a6e526a523d5c01857b772ebe1f332e01e525b1ce7d71df02319cbab22b

Transactions (1)

Coinbasebf3c1a6e526a52…df02319cbab22b

1 in → 115 out10.2000 XPM3.88 KB

ASTyaa89…LKTnQv8K AP7ZfMBN…n8aVFt5X ATt8gWQr…Sp6a6TjB AGdyNhyy…LNSGxpsW AczTyhoV…BMxvtszB

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.

7.779 × 10⁹⁵(96-digit number)

77795837497534531262…78604504921454629759

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

7.779 × 10⁹⁵(96-digit number)

77795837497534531262…78604504921454629759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.779 × 10⁹⁵(96-digit number)

77795837497534531262…78604504921454629761

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

1.555 × 10⁹⁶(97-digit number)

15559167499506906252…57209009842909259519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.555 × 10⁹⁶(97-digit number)

15559167499506906252…57209009842909259521

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

3.111 × 10⁹⁶(97-digit number)

31118334999013812504…14418019685818519039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.111 × 10⁹⁶(97-digit number)

31118334999013812504…14418019685818519041

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

6.223 × 10⁹⁶(97-digit number)

62236669998027625009…28836039371637038079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.223 × 10⁹⁶(97-digit number)

62236669998027625009…28836039371637038081

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

1.244 × 10⁹⁷(98-digit number)

12447333999605525001…57672078743274076159

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