Block #492,590

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/15/2014, 5:59:17 AM · Difficulty 10.6883 · 6,302,971 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

443f393fd54716957dd2c443800beb0a435be0b99560cd8888b0764bf0076f5b

View on Chainz ↗

Height

#492,590

Difficulty

10.688259

Transactions

Size

661 B

Version

Bits

0ab031c5

Nonce

39,362

Timestamp

4/15/2014, 5:59:17 AM

Confirmations

6,302,971

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

06e468a32420d8216613d1bd9f946be25bd8183d183887c1611c33d9a555014c

Transactions (3)

Coinbase1e43254c685004…5bb2f9e2f5de3f

1 in → 1 out8.7600 XPM116 B

AbwWkWZt…kawDhufa

c16ceb5453b0d2…5f8e261cfb5381

1 in → 2 out6.7488 XPM226 B

AKsjVX3m…TT97AJHz AUfZq9jz…xEGBvByx

b3a3211ca803ea…7fe4016dc80c5c

1 in → 2 out1.8237 XPM226 B

ARKAVBJV…1cgvGs3y AbGuiVyt…Fz9Q4tHn

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.

4.814 × 10¹⁰¹(102-digit number)

48144844556246428644…28738445069912345599

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

4.814 × 10¹⁰¹(102-digit number)

48144844556246428644…28738445069912345599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.814 × 10¹⁰¹(102-digit number)

48144844556246428644…28738445069912345601

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

9.628 × 10¹⁰¹(102-digit number)

96289689112492857288…57476890139824691199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.628 × 10¹⁰¹(102-digit number)

96289689112492857288…57476890139824691201

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

1.925 × 10¹⁰²(103-digit number)

19257937822498571457…14953780279649382399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.925 × 10¹⁰²(103-digit number)

19257937822498571457…14953780279649382401

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

3.851 × 10¹⁰²(103-digit number)

38515875644997142915…29907560559298764799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.851 × 10¹⁰²(103-digit number)

38515875644997142915…29907560559298764801

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

7.703 × 10¹⁰²(103-digit number)

77031751289994285830…59815121118597529599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.703 × 10¹⁰²(103-digit number)

77031751289994285830…59815121118597529601

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