Block #2,822,474

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/3/2018, 6:51:29 AM · Difficulty 11.7030 · 4,011,320 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b7329f80011d01ada1576349e1446d8ad0fe94c81942ddb691ffed3c6a44442c

View on Chainz ↗

Height

#2,822,474

Difficulty

11.703037

Transactions

Size

689 B

Version

Bits

0bb3fa39

Nonce

659,690,455

Timestamp

9/3/2018, 6:51:29 AM

Confirmations

4,011,320

Mined by

⛏️ P2SHATnbHb1j6dS6ZbAZjnMveYyXEdbRjm1iAs

Merkle Root

d0b072ccebd4654b4ba9d26863a8d9b8ed7e15cdcf31ecf000932cace1ce545d

Transactions (2)

Coinbasef6ff459c7a3995…f42ee197eba204

1 in → 1 out7.3000 XPM110 B

ATnbHb1j…bRjm1iAs

9c62d10050e465…54dbe01ba8a56c

3 in → 2 out10.1100 XPM489 B

AUQToZpx…zFHyeEQK AaEuhsCJ…fcJX1ePF

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.

6.874 × 10⁹³(94-digit number)

68746722099757682292…58676940592447146299

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

6.874 × 10⁹³(94-digit number)

68746722099757682292…58676940592447146299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.874 × 10⁹³(94-digit number)

68746722099757682292…58676940592447146301

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

1.374 × 10⁹⁴(95-digit number)

13749344419951536458…17353881184894292599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.374 × 10⁹⁴(95-digit number)

13749344419951536458…17353881184894292601

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

2.749 × 10⁹⁴(95-digit number)

27498688839903072917…34707762369788585199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.749 × 10⁹⁴(95-digit number)

27498688839903072917…34707762369788585201

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

5.499 × 10⁹⁴(95-digit number)

54997377679806145834…69415524739577170399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.499 × 10⁹⁴(95-digit number)

54997377679806145834…69415524739577170401

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

1.099 × 10⁹⁵(96-digit number)

10999475535961229166…38831049479154340799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.099 × 10⁹⁵(96-digit number)

10999475535961229166…38831049479154340801

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.199 × 10⁹⁵(96-digit number)

21998951071922458333…77662098958308681599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,822,474

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