Block #498,530

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/18/2014, 3:53:52 AM · Difficulty 10.7805 · 6,309,361 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

051b2a2e5f2d48120136e0b007747f02a36ee323816ec64f2cbbaadff3890e22

View on Chainz ↗

Height

#498,530

Difficulty

10.780479

Transactions

Size

955 B

Version

Bits

0ac7cd7b

Nonce

42,926,301

Timestamp

4/18/2014, 3:53:52 AM

Confirmations

6,309,361

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

75ba09efa0345b55066091a14ac7c45cd10e0e8a8a37e40327b4addf09dcb45a

Transactions (3)

Coinbase1866c3e1816343…163d2b1a92304d

1 in → 1 out8.6100 XPM116 B

AbwWkWZt…kawDhufa

c8120c402564c8…39f41b0952657e

1 in → 2 out0.9443 XPM226 B

APHx196W…DwkgXfoX ALmvPNtU…mjoo7CYQ

ca426686129f64…bb17f32b329a40

3 in → 2 out1.2072 XPM522 B

AGcSEzzc…FhTyc6J8 AcMNnCDo…btimwL4a

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.

5.698 × 10⁹⁷(98-digit number)

56984606051749563861…13279137580452420079

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

5.698 × 10⁹⁷(98-digit number)

56984606051749563861…13279137580452420079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.698 × 10⁹⁷(98-digit number)

56984606051749563861…13279137580452420081

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

1.139 × 10⁹⁸(99-digit number)

11396921210349912772…26558275160904840159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.139 × 10⁹⁸(99-digit number)

11396921210349912772…26558275160904840161

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

2.279 × 10⁹⁸(99-digit number)

22793842420699825544…53116550321809680319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.279 × 10⁹⁸(99-digit number)

22793842420699825544…53116550321809680321

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

4.558 × 10⁹⁸(99-digit number)

45587684841399651089…06233100643619360639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.558 × 10⁹⁸(99-digit number)

45587684841399651089…06233100643619360641

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

9.117 × 10⁹⁸(99-digit number)

91175369682799302179…12466201287238721279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.117 × 10⁹⁸(99-digit number)

91175369682799302179…12466201287238721281

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 #498,530

Cookie Preferences