Block #518,280

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2014, 12:02:37 PM · Difficulty 10.8532 · 6,285,207 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

32325b2a0005fff5067174fedfa5dd35b00c773d57b81a677c70400f552eae0d

View on Chainz ↗

Height

#518,280

Difficulty

10.853221

Transactions

Size

660 B

Version

Bits

0ada6cb8

Nonce

250,332,826

Timestamp

4/30/2014, 12:02:37 PM

Confirmations

6,285,207

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

83bd4be45b4f01d516230896cad1966397f40d69e7ca9e77613b41125ae6881e

Transactions (3)

Coinbase47a94eb6b68cd9…967843bf124635

1 in → 1 out8.5000 XPM116 B

AbwWkWZt…kawDhufa

e8effe22661890…b3a4dd85a3115c

1 in → 2 out4.4463 XPM227 B

AHm4uyXY…gQ6Hg1U2 Ad8ouZVy…Agtc4Bzk

18a53f6168cd3c…637b0a1d00f29e

1 in → 2 out3.6519 XPM226 B

AG8u7ddV…cU5QJSqk AJXJBkhF…LsYEnPjC

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.

2.251 × 10⁹⁷(98-digit number)

22510021744394025698…94066242728345226159

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

2.251 × 10⁹⁷(98-digit number)

22510021744394025698…94066242728345226159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.251 × 10⁹⁷(98-digit number)

22510021744394025698…94066242728345226161

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

4.502 × 10⁹⁷(98-digit number)

45020043488788051396…88132485456690452319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.502 × 10⁹⁷(98-digit number)

45020043488788051396…88132485456690452321

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

9.004 × 10⁹⁷(98-digit number)

90040086977576102793…76264970913380904639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.004 × 10⁹⁷(98-digit number)

90040086977576102793…76264970913380904641

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

1.800 × 10⁹⁸(99-digit number)

18008017395515220558…52529941826761809279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.800 × 10⁹⁸(99-digit number)

18008017395515220558…52529941826761809281

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

3.601 × 10⁹⁸(99-digit number)

36016034791030441117…05059883653523618559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.601 × 10⁹⁸(99-digit number)

36016034791030441117…05059883653523618561

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