Block #1,816,017

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/20/2016, 3:27:15 PM · Difficulty 10.8001 · 5,027,519 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b086f789676579a400d7544b214c3733e7943c6e815d6470dc5a2ef93db58eb

View on Chainz ↗

Height

#1,816,017

Difficulty

10.800130

Transactions

Size

2.98 KB

Version

Bits

0accd54a

Nonce

28,610,978

Timestamp

10/20/2016, 3:27:15 PM

Confirmations

5,027,519

Mined by

⛏️ P2SHAbu3pymUaYvcUp9yc92N8raZy2bPC9RHBm

Merkle Root

51907a13ef8d5e3b56de6ed030e9955f58ea163f9c2d0743b7c07aadf15afe46

Transactions (2)

Coinbase1401a41a44b58e…e05ac301b74c9d

1 in → 1 out8.5900 XPM110 B

Abu3pymU…bPC9RHBm

398b5626055ed2…d1d12086f64eab

19 in → 1 out75.9700 XPM2.79 KB

AVtWEnxx…nytVBavj

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.

4.582 × 10⁹³(94-digit number)

45820550773200295266…59407558498230271879

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

4.582 × 10⁹³(94-digit number)

45820550773200295266…59407558498230271879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.582 × 10⁹³(94-digit number)

45820550773200295266…59407558498230271881

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

9.164 × 10⁹³(94-digit number)

91641101546400590533…18815116996460543759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.164 × 10⁹³(94-digit number)

91641101546400590533…18815116996460543761

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

1.832 × 10⁹⁴(95-digit number)

18328220309280118106…37630233992921087519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.832 × 10⁹⁴(95-digit number)

18328220309280118106…37630233992921087521

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

3.665 × 10⁹⁴(95-digit number)

36656440618560236213…75260467985842175039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.665 × 10⁹⁴(95-digit number)

36656440618560236213…75260467985842175041

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

7.331 × 10⁹⁴(95-digit number)

73312881237120472426…50520935971684350079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.331 × 10⁹⁴(95-digit number)

73312881237120472426…50520935971684350081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #1,816,017

Cookie Preferences