Block #504,969

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/22/2014, 3:28:14 AM · Difficulty 10.8098 · 6,308,060 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

650def799071d241416b73387f8636db6abec6b8b20d06c2cdce66a09878b037

View on Chainz ↗

Height

#504,969

Difficulty

10.809839

Transactions

Size

401 B

Version

Bits

0acf5198

Nonce

7,661,528

Timestamp

4/22/2014, 3:28:14 AM

Confirmations

6,308,060

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c1ae972faee81d602b4da1b8519a75d2901d8904711835523007de8f855172e4

Transactions (2)

Coinbase85193991b4137e…252767b4cbc527

1 in → 1 out8.5500 XPM116 B

AbwWkWZt…kawDhufa

9aecb31682fba6…253ed94e1776d2

1 in → 1 out2.9910 XPM193 B

AXCNJAvq…qsPtg17V

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.

2.740 × 10⁹⁹(100-digit number)

27405148781338670059…72558238024884468479

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

2.740 × 10⁹⁹(100-digit number)

27405148781338670059…72558238024884468479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.740 × 10⁹⁹(100-digit number)

27405148781338670059…72558238024884468481

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

5.481 × 10⁹⁹(100-digit number)

54810297562677340119…45116476049768936959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.481 × 10⁹⁹(100-digit number)

54810297562677340119…45116476049768936961

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

1.096 × 10¹⁰⁰(101-digit number)

10962059512535468023…90232952099537873919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.096 × 10¹⁰⁰(101-digit number)

10962059512535468023…90232952099537873921

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

2.192 × 10¹⁰⁰(101-digit number)

21924119025070936047…80465904199075747839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.192 × 10¹⁰⁰(101-digit number)

21924119025070936047…80465904199075747841

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

4.384 × 10¹⁰⁰(101-digit number)

43848238050141872095…60931808398151495679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.384 × 10¹⁰⁰(101-digit number)

43848238050141872095…60931808398151495681

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 #504,969

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