Block #533,671

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/9/2014, 8:42:17 PM · Difficulty 10.9001 · 6,269,476 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ee727e683869c052f5c47e58f3ab0b5a2794a8775ee9f58191bfbe0d8c1963f0

View on Chainz ↗

Height

#533,671

Difficulty

10.900130

Transactions

Size

766 B

Version

Bits

0ae66ee4

Nonce

106,104

Timestamp

5/9/2014, 8:42:17 PM

Confirmations

6,269,476

Mined by

⛏️ $aSm=AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5eefeaf5f32dcc3b1538e72ab314fc12ce3a3d8672530a92fc6b55074a195ff6

Transactions (1)

Coinbase5eefeaf5f32dcc…6b55074a195ff6

1 in → 18 out8.4000 XPM675 B

AQvZBsUo…hppgRZTJ AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j Ae7UyoY4…DtgAv9cY

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.

1.411 × 10⁹⁸(99-digit number)

14113719413140929613…12712814143607470079

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

1.411 × 10⁹⁸(99-digit number)

14113719413140929613…12712814143607470079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.411 × 10⁹⁸(99-digit number)

14113719413140929613…12712814143607470081

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

2.822 × 10⁹⁸(99-digit number)

28227438826281859227…25425628287214940159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.822 × 10⁹⁸(99-digit number)

28227438826281859227…25425628287214940161

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

5.645 × 10⁹⁸(99-digit number)

56454877652563718455…50851256574429880319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.645 × 10⁹⁸(99-digit number)

56454877652563718455…50851256574429880321

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

1.129 × 10⁹⁹(100-digit number)

11290975530512743691…01702513148859760639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.129 × 10⁹⁹(100-digit number)

11290975530512743691…01702513148859760641

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

2.258 × 10⁹⁹(100-digit number)

22581951061025487382…03405026297719521279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.258 × 10⁹⁹(100-digit number)

22581951061025487382…03405026297719521281

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