Block #2,524,834

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/17/2018, 4:18:03 AM · Difficulty 10.9833 · 4,317,392 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a7f579a8dd0ea24c83ec919213c2b3aa97577f2f40c64349fbafe6f361d62058

View on Chainz ↗

Height

#2,524,834

Difficulty

10.983281

Transactions

Size

507 B

Version

Bits

0afbb84e

Nonce

217,892,772

Timestamp

2/17/2018, 4:18:03 AM

Confirmations

4,317,392

Mined by

⛏️ P2SHAUyftNMEhAVu9CEi3NCypPZUAdg8oPnL97

Merkle Root

a028c7056df269a32e99e63bbd4f0e568613a3bd74339107fad2f58999368faf

Transactions (2)

Coinbasea7c0b7c3efae69…bc04bb912410f3

1 in → 1 out8.2900 XPM110 B

AUyftNME…g8oPnL97

4c864f7b7b7f12…562934042ede26

2 in → 2 out16.5500 XPM306 B

AGoYowqV…s8a6cKpk AQW4sYpK…ajMoSNuH

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.

1.498 × 10⁹⁷(98-digit number)

14986782457408497816…16810641050492282879

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

1.498 × 10⁹⁷(98-digit number)

14986782457408497816…16810641050492282879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.498 × 10⁹⁷(98-digit number)

14986782457408497816…16810641050492282881

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

2.997 × 10⁹⁷(98-digit number)

29973564914816995632…33621282100984565759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.997 × 10⁹⁷(98-digit number)

29973564914816995632…33621282100984565761

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

5.994 × 10⁹⁷(98-digit number)

59947129829633991264…67242564201969131519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.994 × 10⁹⁷(98-digit number)

59947129829633991264…67242564201969131521

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

1.198 × 10⁹⁸(99-digit number)

11989425965926798252…34485128403938263039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.198 × 10⁹⁸(99-digit number)

11989425965926798252…34485128403938263041

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

2.397 × 10⁹⁸(99-digit number)

23978851931853596505…68970256807876526079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.397 × 10⁹⁸(99-digit number)

23978851931853596505…68970256807876526081

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

4.795 × 10⁹⁸(99-digit number)

47957703863707193011…37940513615753052159

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 #2,524,834

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