Block #204,821

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/11/2013, 6:09:53 PM · Difficulty 9.8991 · 6,602,238 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d6bc1d728d79df6d4f0584c5a5b97802dffbd21ea94914c6a2b28b04657d8feb

View on Chainz ↗

Height

#204,821

Difficulty

9.899105

Transactions

Size

652 B

Version

Bits

09e62bc4

Nonce

24,739

Timestamp

10/11/2013, 6:09:53 PM

Confirmations

6,602,238

Mined by

⛏️ P2SHAPixL4rLnxX9Uz1oM8ndN2sAjkjhCzHXd7

Merkle Root

421ff7319c0cdd648feefcc7d074ea8898630201ad8a39128a72533c71057b26

Transactions (3)

Coinbase55a5a20c985ddd…89fb7a2cd9a64b

1 in → 1 out10.2100 XPM109 B

APixL4rL…jhCzHXd7

cb0a33f0646499…cb38e70642096c

1 in → 2 out10.1900 XPM226 B

AWuYcCxG…13CL5z4e AQyuBu3M…gbuPvBK6

9e55e01812f334…9ca48135eff0d4

1 in → 2 out6.1575 XPM226 B

AYngBNPM…nxQ2J1w9 AXS4sCsQ…dQko7TSJ

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.

1.083 × 10⁹⁶(97-digit number)

10830698030343497026…37169700538473983999

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

1.083 × 10⁹⁶(97-digit number)

10830698030343497026…37169700538473983999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.083 × 10⁹⁶(97-digit number)

10830698030343497026…37169700538473984001

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

2.166 × 10⁹⁶(97-digit number)

21661396060686994053…74339401076947967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.166 × 10⁹⁶(97-digit number)

21661396060686994053…74339401076947968001

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

4.332 × 10⁹⁶(97-digit number)

43322792121373988107…48678802153895935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.332 × 10⁹⁶(97-digit number)

43322792121373988107…48678802153895936001

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

8.664 × 10⁹⁶(97-digit number)

86645584242747976215…97357604307791871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.664 × 10⁹⁶(97-digit number)

86645584242747976215…97357604307791872001

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

1.732 × 10⁹⁷(98-digit number)

17329116848549595243…94715208615583743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.732 × 10⁹⁷(98-digit number)

17329116848549595243…94715208615583744001

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 #204,821

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