Block #2,778,726

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/4/2018, 11:18:56 AM · Difficulty 11.6493 · 4,062,811 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef827a0a675904b46b176837e061ff1764ca7bd40950dd874a5c337492d92093

View on Chainz ↗

Height

#2,778,726

Difficulty

11.649330

Transactions

Size

2.73 KB

Version

Bits

0ba63a7e

Nonce

1,778,277,620

Timestamp

8/4/2018, 11:18:56 AM

Confirmations

4,062,811

Mined by

⛏️ P2SHAUw14pmpejLpYDZP3pqfvE7jyj4m5NDrKT

Merkle Root

ce1d665a9a5c72b0ceaf3312df152928a842468320c9ad44d8fabad0553108c8

Transactions (2)

Coinbased9818c88b8e8ff…e7c548f68c5dbc

1 in → 1 out7.3900 XPM110 B

AUw14pmp…4m5NDrKT

41338d2a7d816a…3bdb654e14fa24

17 in → 2 out10163.3442 XPM2.53 KB

AWktDgJA…jXBcWkfs Aek4ofV3…M6GBS6AU

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.

3.619 × 10⁹⁷(98-digit number)

36198310108474947692…78204803082275307519

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

3.619 × 10⁹⁷(98-digit number)

36198310108474947692…78204803082275307519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.619 × 10⁹⁷(98-digit number)

36198310108474947692…78204803082275307521

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

7.239 × 10⁹⁷(98-digit number)

72396620216949895385…56409606164550615039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.239 × 10⁹⁷(98-digit number)

72396620216949895385…56409606164550615041

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

1.447 × 10⁹⁸(99-digit number)

14479324043389979077…12819212329101230079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.447 × 10⁹⁸(99-digit number)

14479324043389979077…12819212329101230081

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

2.895 × 10⁹⁸(99-digit number)

28958648086779958154…25638424658202460159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.895 × 10⁹⁸(99-digit number)

28958648086779958154…25638424658202460161

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

5.791 × 10⁹⁸(99-digit number)

57917296173559916308…51276849316404920319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.791 × 10⁹⁸(99-digit number)

57917296173559916308…51276849316404920321

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

1.158 × 10⁹⁹(100-digit number)

11583459234711983261…02553698632809840639

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 #2,778,726

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