Block #2,690,917

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/4/2018, 1:45:30 AM · Difficulty 11.6863 · 4,141,667 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

56be51c470b43bf896c8d75ea9aab1492c4710ab148072c4bf128270baafcae4

View on Chainz ↗

Height

#2,690,917

Difficulty

11.686305

Transactions

Size

1.12 KB

Version

Bits

0bafb1b3

Nonce

1,130,412,244

Timestamp

6/4/2018, 1:45:30 AM

Confirmations

4,141,667

Mined by

⛏️ P2SHASKZtgNwBi8ByhL6gYfzJR2euaoEb1GuZf

Merkle Root

5327eba3469a50b249a003a9a7c3d0f233c04841d70daed28ccdcde57310ed25

Transactions (4)

Coinbaseebd44fc79cf2fb…315f65cf24443b

1 in → 1 out7.3400 XPM110 B

ASKZtgNw…oEb1GuZf

cc0e403fd778d7…a70c0946948a4c

2 in → 2 out14.6700 XPM305 B

AQ7S9cWe…rDsLcCRa AZPhwjJK…7yxgMgZ7

d3190695382e54…bf6452a971aa17

2 in → 2 out14.6300 XPM306 B

AKfN5ELc…A3YNDXZ8 AVuNEeXm…weqPuRWv

dd89c59eeadabf…331dec6836ca3f

2 in → 2 out11.9400 XPM339 B

AJrzQptm…RTcdytmQ Aei7Ymdr…MjKXcgCp

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.

3.234 × 10⁹⁷(98-digit number)

32349816355543307791…02480925610048307199

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

3.234 × 10⁹⁷(98-digit number)

32349816355543307791…02480925610048307199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.234 × 10⁹⁷(98-digit number)

32349816355543307791…02480925610048307201

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

6.469 × 10⁹⁷(98-digit number)

64699632711086615583…04961851220096614399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.469 × 10⁹⁷(98-digit number)

64699632711086615583…04961851220096614401

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

1.293 × 10⁹⁸(99-digit number)

12939926542217323116…09923702440193228799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.293 × 10⁹⁸(99-digit number)

12939926542217323116…09923702440193228801

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

2.587 × 10⁹⁸(99-digit number)

25879853084434646233…19847404880386457599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.587 × 10⁹⁸(99-digit number)

25879853084434646233…19847404880386457601

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

5.175 × 10⁹⁸(99-digit number)

51759706168869292466…39694809760772915199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.175 × 10⁹⁸(99-digit number)

51759706168869292466…39694809760772915201

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

1.035 × 10⁹⁹(100-digit number)

10351941233773858493…79389619521545830399

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 #2,690,917

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