Block #282,585

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 10:47:40 AM · Difficulty 9.9793 · 6,524,387 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

773c414cba993415cfd77daa0acd53b5048df37f67adcface8218a908cf55446

View on Chainz ↗

Height

#282,585

Difficulty

9.979303

Transactions

Size

2.70 KB

Version

Bits

09fab394

Nonce

96,111

Timestamp

11/29/2013, 10:47:40 AM

Confirmations

6,524,387

Mined by

⛏️ OaRpAGFAJ5YLhSEKHJ6SLzkv6wy6PiZEnBbk6G

Merkle Root

00791c37bdac944968d3f360ec2b7bc5016d5828d07c4845331339e242a7864f

Transactions (2)

Coinbase6f99730969a29f…a6fbb8225acb09

1 in → 31 out10.0100 XPM1.09 KB

AGFAJ5YL…ZEnBbk6G AZ2pPuKg…95SN2Yr7 AZZtaVxj…niydt4kE AWXYBWKP…qQAoisBJ AQyr8Lw3…hs4nt3Pn

8b3c5405deb779…f66d3f3c87c62e

10 in → 2 out20.7075 XPM1.52 KB

AYFNbij4…1kw8ctBR Adb1BMS7…fEoQFzmX

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.

1.719 × 10⁹⁵(96-digit number)

17195156988648895444…27678115239912403499

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

1.719 × 10⁹⁵(96-digit number)

17195156988648895444…27678115239912403499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.719 × 10⁹⁵(96-digit number)

17195156988648895444…27678115239912403501

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

3.439 × 10⁹⁵(96-digit number)

34390313977297790888…55356230479824806999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.439 × 10⁹⁵(96-digit number)

34390313977297790888…55356230479824807001

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

6.878 × 10⁹⁵(96-digit number)

68780627954595581777…10712460959649613999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.878 × 10⁹⁵(96-digit number)

68780627954595581777…10712460959649614001

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

1.375 × 10⁹⁶(97-digit number)

13756125590919116355…21424921919299227999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.375 × 10⁹⁶(97-digit number)

13756125590919116355…21424921919299228001

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

2.751 × 10⁹⁶(97-digit number)

27512251181838232711…42849843838598455999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.751 × 10⁹⁶(97-digit number)

27512251181838232711…42849843838598456001

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 #282,585

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