Block #524,989

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/4/2014, 12:15:45 PM · Difficulty 10.8783 · 6,264,981 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e173df0d1aed0ae634b1533e0b8b4d6749e78df776cf6b5b2834d0bed19e5742

View on Chainz ↗

Height

#524,989

Difficulty

10.878325

Transactions

Size

728 B

Version

Bits

0ae0d9e5

Nonce

230,272,129

Timestamp

5/4/2014, 12:15:45 PM

Confirmations

6,264,981

Merkle Root

ec4867ef929ad9c50e12920d6d44b118ee352a43c10144df7873f2d0bbf642b1

Transactions (2)

Coinbase2ffe35e5a28505…ab906b3a9b9a5a

1 in → 1 out8.4500 XPM116 B

AbwWkWZt…kawDhufa

3d27d6e4cfa835…bd7a0e4a5d11e5

3 in → 2 out639.5760 XPM520 B

AGMU9iGJ…xXvB7cGX AR7JmyAc…dudNciZo

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.

1.638 × 10⁹⁸(99-digit number)

16384799473700963400…82820779045486536379

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

1.638 × 10⁹⁸(99-digit number)

16384799473700963400…82820779045486536379

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.638 × 10⁹⁸(99-digit number)

16384799473700963400…82820779045486536381

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

3.276 × 10⁹⁸(99-digit number)

32769598947401926801…65641558090973072759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.276 × 10⁹⁸(99-digit number)

32769598947401926801…65641558090973072761

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

6.553 × 10⁹⁸(99-digit number)

65539197894803853602…31283116181946145519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.553 × 10⁹⁸(99-digit number)

65539197894803853602…31283116181946145521

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

1.310 × 10⁹⁹(100-digit number)

13107839578960770720…62566232363892291039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.310 × 10⁹⁹(100-digit number)

13107839578960770720…62566232363892291041

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

2.621 × 10⁹⁹(100-digit number)

26215679157921541440…25132464727784582079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.621 × 10⁹⁹(100-digit number)

26215679157921541440…25132464727784582081

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