Block #192,772

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 2:23:02 AM · Difficulty 9.8750 · 6,599,258 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

da009cc4cf94be450afa115c78e644d6c7d1e623616f4e3356814553ff23f106

View on Chainz ↗

Height

#192,772

Difficulty

9.874985

Transactions

Size

198 B

Version

Bits

09dfff02

Nonce

6,334

Timestamp

10/4/2013, 2:23:02 AM

Confirmations

6,599,258

Merkle Root

a95784eec17e50a322a0ecb78a9d2f7acb06d19d7d39a38e3b70587825fa6b99

Transactions (1)

Coinbasea95784eec17e50…70587825fa6b99

1 in → 1 out10.2400 XPM109 B

Af4wD75X…Lxgjq8Ud

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.

2.005 × 10⁹²(93-digit number)

20056346477369362885…78686892755296616399

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

2.005 × 10⁹²(93-digit number)

20056346477369362885…78686892755296616399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.005 × 10⁹²(93-digit number)

20056346477369362885…78686892755296616401

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

4.011 × 10⁹²(93-digit number)

40112692954738725770…57373785510593232799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.011 × 10⁹²(93-digit number)

40112692954738725770…57373785510593232801

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

8.022 × 10⁹²(93-digit number)

80225385909477451541…14747571021186465599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.022 × 10⁹²(93-digit number)

80225385909477451541…14747571021186465601

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

1.604 × 10⁹³(94-digit number)

16045077181895490308…29495142042372931199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.604 × 10⁹³(94-digit number)

16045077181895490308…29495142042372931201

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

3.209 × 10⁹³(94-digit number)

32090154363790980616…58990284084745862399

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