Block #190,327

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/2/2013, 10:30:59 AM · Difficulty 9.8734 · 6,608,608 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f85a1aac17963a4a55f192b22dcd84b9658ca237d2b25bc321e01d038ab2e8d

View on Chainz ↗

Height

#190,327

Difficulty

9.873379

Transactions

Size

550 B

Version

Bits

09df95c9

Nonce

141,353

Timestamp

10/2/2013, 10:30:59 AM

Confirmations

6,608,608

Mined by

⛏️ P2SHAVe57QvQ1vCrcfixxmQzmm7HCK3A6qu7RC

Merkle Root

c454e5b7a547fed2c8590ac1cb5020ee862284ab37e2e10e2e7550ed8028c6dd

Transactions (3)

Coinbasef9a8461c72a2c8…96e33165fd216b

1 in → 1 out10.2600 XPM109 B

AVe57QvQ…3A6qu7RC

6da47253dbf7dc…7514b799f95533

1 in → 1 out12.4600 XPM157 B

ARnEvJFf…rKa3CSt1

7f85f5dfa6b20c…dbad1b2e4090c6

1 in → 2 out10.2500 XPM193 B

ALRDixNE…vCoYGXar AbTVxWeW…ncXhWXRV

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.

1.295 × 10⁹⁸(99-digit number)

12954209273072804929…23491754017642243519

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

1.295 × 10⁹⁸(99-digit number)

12954209273072804929…23491754017642243519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.295 × 10⁹⁸(99-digit number)

12954209273072804929…23491754017642243521

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

2.590 × 10⁹⁸(99-digit number)

25908418546145609859…46983508035284487039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.590 × 10⁹⁸(99-digit number)

25908418546145609859…46983508035284487041

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

5.181 × 10⁹⁸(99-digit number)

51816837092291219718…93967016070568974079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.181 × 10⁹⁸(99-digit number)

51816837092291219718…93967016070568974081

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

1.036 × 10⁹⁹(100-digit number)

10363367418458243943…87934032141137948159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.036 × 10⁹⁹(100-digit number)

10363367418458243943…87934032141137948161

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

2.072 × 10⁹⁹(100-digit number)

20726734836916487887…75868064282275896319

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