Block #2,758,043

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/20/2018, 9:56:13 PM · Difficulty 11.6675 · 4,084,382 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

002f41028d0c5de6a4109b99d75f59033903ee5f4788cf62dc68309ca0db8fa7

View on Chainz ↗

Height

#2,758,043

Difficulty

11.667474

Transactions

Size

1.00 KB

Version

Bits

0baadf94

Nonce

373,336,262

Timestamp

7/20/2018, 9:56:13 PM

Confirmations

4,084,382

Mined by

⛏️ P2SHAZnNQqbqLUWZqZa3rgHUyTMsLkYjphfRGF

Merkle Root

2610c28fe2343eb9a7ca8a20cc6fe496f642b5ea5eae38fff5ca31ef8ea26ae6

Transactions (3)

Coinbasedbfd3a28226b77…68bc164f5c837f

1 in → 1 out7.3500 XPM109 B

AZnNQqbq…YjphfRGF

f38c9cd2bc1d61…1cc4ca624dbb7c

2 in → 2 out12.0300 XPM341 B

ASN2yCkU…2sMQupwT ASpEbXwS…YG6Eey3V

fe772f410264e0…bfc6f0d0123c2c

3 in → 2 out10.7600 XPM487 B

ATq7n7ij…Pa2iM82C ANEq6Gdi…Pbk4HtRv

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.

1.859 × 10⁹⁵(96-digit number)

18597577020236458228…76427955274403593599

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

1.859 × 10⁹⁵(96-digit number)

18597577020236458228…76427955274403593599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.859 × 10⁹⁵(96-digit number)

18597577020236458228…76427955274403593601

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

3.719 × 10⁹⁵(96-digit number)

37195154040472916456…52855910548807187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.719 × 10⁹⁵(96-digit number)

37195154040472916456…52855910548807187201

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

7.439 × 10⁹⁵(96-digit number)

74390308080945832912…05711821097614374399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.439 × 10⁹⁵(96-digit number)

74390308080945832912…05711821097614374401

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

1.487 × 10⁹⁶(97-digit number)

14878061616189166582…11423642195228748799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.487 × 10⁹⁶(97-digit number)

14878061616189166582…11423642195228748801

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

2.975 × 10⁹⁶(97-digit number)

29756123232378333164…22847284390457497599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.975 × 10⁹⁶(97-digit number)

29756123232378333164…22847284390457497601

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

5.951 × 10⁹⁶(97-digit number)

59512246464756666329…45694568780914995199

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 #2,758,043

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