Block #191,878

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/3/2013, 11:15:29 AM · Difficulty 9.8753 · 6,618,870 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b301b68dd2c75ede7e6e56e4d4784ecc7afa98919840d674efac6bcdb42bf2cd

View on Chainz ↗

Height

#191,878

Difficulty

9.875282

Transactions

Size

3.57 KB

Version

Bits

09e01274

Nonce

1,164,796,862

Timestamp

10/3/2013, 11:15:29 AM

Confirmations

6,618,870

Mined by

⛏️ RMQ"SAGtYEKhSevZpkDNk6aVXE1LkCHmRGWWgRv

Merkle Root

6d020b332ffc9152495638b5a8d635322b5dc9205959837d97f4bf71d2b00fb2

Transactions (1)

Coinbase6d020b332ffc91…f4bf71d2b00fb2

1 in → 103 out10.2000 XPM3.48 KB

AGtYEKhS…mRGWWgRv AL3a8jxK…bf8tx3CC AKRpbXWP…X6DRYUqb AZ4gvP32…ukKsCiYr AVeHc9d8…MRstqd4p

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.

2.080 × 10⁹⁴(95-digit number)

20809107699761901269…43462787615871240639

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

2.080 × 10⁹⁴(95-digit number)

20809107699761901269…43462787615871240639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.080 × 10⁹⁴(95-digit number)

20809107699761901269…43462787615871240641

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

4.161 × 10⁹⁴(95-digit number)

41618215399523802539…86925575231742481279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.161 × 10⁹⁴(95-digit number)

41618215399523802539…86925575231742481281

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

8.323 × 10⁹⁴(95-digit number)

83236430799047605078…73851150463484962559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.323 × 10⁹⁴(95-digit number)

83236430799047605078…73851150463484962561

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

1.664 × 10⁹⁵(96-digit number)

16647286159809521015…47702300926969925119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.664 × 10⁹⁵(96-digit number)

16647286159809521015…47702300926969925121

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

3.329 × 10⁹⁵(96-digit number)

33294572319619042031…95404601853939850239

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

Block #191,878

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