Block #491,244

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2014, 9:40:33 AM · Difficulty 10.6799 · 6,318,105 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e2fa7559819b0beca91e581098e86680d99e76efab4b8b7ab49cac9fc7920db

View on Chainz ↗

Height

#491,244

Difficulty

10.679907

Transactions

Size

1.08 KB

Version

Bits

0aae0e5d

Nonce

1,756

Timestamp

4/14/2014, 9:40:33 AM

Confirmations

6,318,105

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

0bde60e173287a4863876eee036aacfd6aa941bde37fd036c8fb31b226b49e5e

Transactions (5)

Coinbasebfb849b67c100f…5a33b8443bb90a

1 in → 1 out8.7900 XPM116 B

AbwWkWZt…kawDhufa

4d26f6db292b1f…311c4cbffe7a4b

1 in → 2 out1709.3730 XPM226 B

AZopJ8Ka…Y4mwubyi AUZ9mEbj…mekyfpBF

a75de9f623a68b…063e38943feeab

1 in → 2 out9.9900 XPM225 B

ASad3Jji…AiUzoawL AGT9CaN5…AqhMhyGJ

401b80259f9618…3068cfd4d65dbf

1 in → 2 out4.7161 XPM225 B

AZcktv9D…2FzqrKVk AahFQhbu…NgQw6vzQ

e5154005271e68…d4fa8b7cd90eda

1 in → 2 out1.6148 XPM226 B

Ab3ZA77H…R7ktRp2N ASxLCi9F…7z1Ds2HR

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.

6.232 × 10¹⁰⁰(101-digit number)

62325789448605841826…68428494240457932799

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

6.232 × 10¹⁰⁰(101-digit number)

62325789448605841826…68428494240457932799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.232 × 10¹⁰⁰(101-digit number)

62325789448605841826…68428494240457932801

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

1.246 × 10¹⁰¹(102-digit number)

12465157889721168365…36856988480915865599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.246 × 10¹⁰¹(102-digit number)

12465157889721168365…36856988480915865601

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

2.493 × 10¹⁰¹(102-digit number)

24930315779442336730…73713976961831731199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.493 × 10¹⁰¹(102-digit number)

24930315779442336730…73713976961831731201

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

4.986 × 10¹⁰¹(102-digit number)

49860631558884673461…47427953923663462399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.986 × 10¹⁰¹(102-digit number)

49860631558884673461…47427953923663462401

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

9.972 × 10¹⁰¹(102-digit number)

99721263117769346922…94855907847326924799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.972 × 10¹⁰¹(102-digit number)

99721263117769346922…94855907847326924801

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 #491,244

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