Block #2,820,911

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/2/2018, 5:37:25 AM · Difficulty 11.7003 · 4,019,553 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

68d4835b3c3e18b94c8bd7cc7f97ee3bf51ec445df6307c3880c1840c4c65499

View on Chainz ↗

Height

#2,820,911

Difficulty

11.700308

Transactions

Size

3.51 KB

Version

Bits

0bb34768

Nonce

845,812,572

Timestamp

9/2/2018, 5:37:25 AM

Confirmations

4,019,553

Mined by

⛏️ P2SHAJCWUi6jU21DwnWrrAXLGoZW7faGiR5txE

Merkle Root

54dc6c3f611eecfb47f0b1eb93e5a4a61ba93e80b4278b9959b1a6d335f28d8e

Transactions (5)

Coinbase0ffc511216c879…ed91a28ea4c961

1 in → 1 out7.3800 XPM110 B

AJCWUi6j…aGiR5txE

0070fa91bd0669…f38c4fe5266da5

15 in → 2 out17808.8808 XPM2.25 KB

ASagj2DX…Qdnsg6tw AYqUZT5S…Le8qLwx9

5c404c4a3ab6b6…60b8fbdd7088a5

1 in → 2 out7.2900 XPM193 B

AZH17ico…vZ6eUZuV AVLjnD5W…8Cp8fKGF

48678bf54f6046…27d7720d6a305c

2 in → 2 out5.4381 XPM374 B

Acm6hnU5…6ynosv9K ASJZNN3p…iv4QQTBz

3c53c66ae01698…4018c02b83633c

3 in → 2 out1.1937 XPM523 B

ALhuYhvR…rW49jwrh ARMFdT2w…TGxHik4a

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.

1.100 × 10⁹⁴(95-digit number)

11003472609688209981…50544286905647230639

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

1.100 × 10⁹⁴(95-digit number)

11003472609688209981…50544286905647230639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.100 × 10⁹⁴(95-digit number)

11003472609688209981…50544286905647230641

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

2.200 × 10⁹⁴(95-digit number)

22006945219376419963…01088573811294461279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.200 × 10⁹⁴(95-digit number)

22006945219376419963…01088573811294461281

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

4.401 × 10⁹⁴(95-digit number)

44013890438752839926…02177147622588922559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.401 × 10⁹⁴(95-digit number)

44013890438752839926…02177147622588922561

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

8.802 × 10⁹⁴(95-digit number)

88027780877505679852…04354295245177845119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.802 × 10⁹⁴(95-digit number)

88027780877505679852…04354295245177845121

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

1.760 × 10⁹⁵(96-digit number)

17605556175501135970…08708590490355690239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.760 × 10⁹⁵(96-digit number)

17605556175501135970…08708590490355690241

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

3.521 × 10⁹⁵(96-digit number)

35211112351002271940…17417180980711380479

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 #2,820,911

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