Block #517,061

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/29/2014, 5:27:42 PM · Difficulty 10.8501 · 6,295,516 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d4b45833ca980bd6b9c694f9170984c931e5fc416263ee9d3b36041e727b6fa

View on Chainz ↗

Height

#517,061

Difficulty

10.850073

Transactions

Size

799 B

Version

Bits

0ad99e67

Nonce

45,769

Timestamp

4/29/2014, 5:27:42 PM

Confirmations

6,295,516

Mined by

⛏️ aS_#AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

bc00764b0d173f87224c57c1bffa0389f43497cb57bcd8fa6cf55e4ff177bff7

Transactions (1)

Coinbasebc00764b0d173f…f55e4ff177bff7

1 in → 19 out8.4800 XPM709 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AUbecsVa…i8zo8qRf ATKK7iFz…wZm46KN1

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.

1.410 × 10⁹⁴(95-digit number)

14109539401567035431…65676751263729429439

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

1.410 × 10⁹⁴(95-digit number)

14109539401567035431…65676751263729429439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.410 × 10⁹⁴(95-digit number)

14109539401567035431…65676751263729429441

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

2.821 × 10⁹⁴(95-digit number)

28219078803134070862…31353502527458858879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.821 × 10⁹⁴(95-digit number)

28219078803134070862…31353502527458858881

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

5.643 × 10⁹⁴(95-digit number)

56438157606268141725…62707005054917717759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.643 × 10⁹⁴(95-digit number)

56438157606268141725…62707005054917717761

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

1.128 × 10⁹⁵(96-digit number)

11287631521253628345…25414010109835435519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.128 × 10⁹⁵(96-digit number)

11287631521253628345…25414010109835435521

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

2.257 × 10⁹⁵(96-digit number)

22575263042507256690…50828020219670871039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.257 × 10⁹⁵(96-digit number)

22575263042507256690…50828020219670871041

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 #517,061

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