Block #2,442,474

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/26/2017, 3:16:48 PM · Difficulty 10.9314 · 4,388,410 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e56c71fe672ffe2df4a785f758bba3870c840191595e66d7ea0be18728da24c1

View on Chainz ↗

Height

#2,442,474

Difficulty

10.931385

Transactions

Size

426 B

Version

Bits

0aee6f45

Nonce

353,803,540

Timestamp

12/26/2017, 3:16:48 PM

Confirmations

4,388,410

Mined by

⛏️ P2SHAGmtJ2qLuky5dbLheeSgXG99ApojwagWj7

Merkle Root

d96c849f140a22d3100a73471acff80dda57d6c1095473863dbd1a1085651021

Transactions (2)

Coinbase7bc5e60a3cf7dc…88f156cdb3e02e

1 in → 1 out8.3700 XPM110 B

AGmtJ2qL…ojwagWj7

25b8e1b76e89dc…a002d3b8e5a8cf

1 in → 2 out629.7655 XPM226 B

AcX1jXZG…MBdDHGex Ad3FmMmo…Qdw3toT4

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.

1.559 × 10⁹⁴(95-digit number)

15599724455748683265…32444338470065012999

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

1.559 × 10⁹⁴(95-digit number)

15599724455748683265…32444338470065012999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.559 × 10⁹⁴(95-digit number)

15599724455748683265…32444338470065013001

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

3.119 × 10⁹⁴(95-digit number)

31199448911497366531…64888676940130025999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.119 × 10⁹⁴(95-digit number)

31199448911497366531…64888676940130026001

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

6.239 × 10⁹⁴(95-digit number)

62398897822994733062…29777353880260051999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.239 × 10⁹⁴(95-digit number)

62398897822994733062…29777353880260052001

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

1.247 × 10⁹⁵(96-digit number)

12479779564598946612…59554707760520103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.247 × 10⁹⁵(96-digit number)

12479779564598946612…59554707760520104001

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

2.495 × 10⁹⁵(96-digit number)

24959559129197893225…19109415521040207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.495 × 10⁹⁵(96-digit number)

24959559129197893225…19109415521040208001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,442,474

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