Block #192,548

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/3/2013, 10:59:47 PM · Difficulty 9.8745 · 6,611,120 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b781ffb4e638c2320445c2dc83020e028b7a5be378592abe6513f6aac8ede14

View on Chainz ↗

Height

#192,548

Difficulty

9.874501

Transactions

Size

4.17 KB

Version

Bits

09dfdf4d

Nonce

1,164,822,440

Timestamp

10/3/2013, 10:59:47 PM

Confirmations

6,611,120

Mined by

⛏️ $RM2AGdyNhyyugYe7efPm6oJXucH8TLNSGxpsW

Merkle Root

1e724197935d1c837f1b4be4af3e64fb28aebcf49edeff6203bc026849f92ec7

Transactions (1)

Coinbase1e724197935d1c…bc026849f92ec7

1 in → 121 out10.1900 XPM4.08 KB

AGdyNhyy…LNSGxpsW Aabufq6z…vs9soDm5 AWWaDRnP…qR1zB7PV AWJHU8CF…JUjqyNaX AdqZDct3…Y1D432wN

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.

4.751 × 10⁹⁴(95-digit number)

47517910537166516222…54087193754552023039

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

4.751 × 10⁹⁴(95-digit number)

47517910537166516222…54087193754552023039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.751 × 10⁹⁴(95-digit number)

47517910537166516222…54087193754552023041

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

9.503 × 10⁹⁴(95-digit number)

95035821074333032444…08174387509104046079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.503 × 10⁹⁴(95-digit number)

95035821074333032444…08174387509104046081

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

1.900 × 10⁹⁵(96-digit number)

19007164214866606488…16348775018208092159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.900 × 10⁹⁵(96-digit number)

19007164214866606488…16348775018208092161

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

3.801 × 10⁹⁵(96-digit number)

38014328429733212977…32697550036416184319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.801 × 10⁹⁵(96-digit number)

38014328429733212977…32697550036416184321

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

7.602 × 10⁹⁵(96-digit number)

76028656859466425955…65395100072832368639

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