Block #2,668,095

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/19/2018, 8:14:49 AM · Difficulty 11.6745 · 4,174,383 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5142555566c42fa2e1450fccc7849affcddad0316ac0c8208ce95bd21ee02c36

View on Chainz ↗

Height

#2,668,095

Difficulty

11.674530

Transactions

Size

1020 B

Version

Bits

0bacadfb

Nonce

515,432,494

Timestamp

5/19/2018, 8:14:49 AM

Confirmations

4,174,383

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

6d7b06095b516e524de198971abe0180f3fa552fc1dae93afcd8569bddc689de

Transactions (2)

Coinbase28506d8782fedd…d5b36ac5b50ce2

1 in → 1 out7.3300 XPM110 B

Adqah8zh…1WwoHJ9t

a35edb0dc5f56b…6bac42578e0509

5 in → 2 out9965.8301 XPM820 B

Ab6UyKEz…LmgCrzrn ATGPBLmo…CFXDY7bV

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.

1.866 × 10⁹⁴(95-digit number)

18666427428986621981…31842507616970146079

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

1.866 × 10⁹⁴(95-digit number)

18666427428986621981…31842507616970146079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.866 × 10⁹⁴(95-digit number)

18666427428986621981…31842507616970146081

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

3.733 × 10⁹⁴(95-digit number)

37332854857973243962…63685015233940292159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.733 × 10⁹⁴(95-digit number)

37332854857973243962…63685015233940292161

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

7.466 × 10⁹⁴(95-digit number)

74665709715946487924…27370030467880584319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.466 × 10⁹⁴(95-digit number)

74665709715946487924…27370030467880584321

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

1.493 × 10⁹⁵(96-digit number)

14933141943189297584…54740060935761168639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.493 × 10⁹⁵(96-digit number)

14933141943189297584…54740060935761168641

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

2.986 × 10⁹⁵(96-digit number)

29866283886378595169…09480121871522337279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.986 × 10⁹⁵(96-digit number)

29866283886378595169…09480121871522337281

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

5.973 × 10⁹⁵(96-digit number)

59732567772757190339…18960243743044674559

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 #2,668,095

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