Block #282,397

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 9:05:32 AM · Difficulty 9.9790 · 6,532,071 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bc3a86660de6ed7a36e763e316d76e695c1c3dcca859d07007d07d5fb0937e9f

View on Chainz ↗

Height

#282,397

Difficulty

9.979017

Transactions

Size

1.72 KB

Version

Bits

09faa0db

Nonce

43,749

Timestamp

11/29/2013, 9:05:32 AM

Confirmations

6,532,071

Mined by

⛏️ OaRZ+AGFAJ5YLhSEKHJ6SLzkv6wy6PiZEnBbk6G

Merkle Root

5cacf56c592218fd8fdc8aff5aeab16ed7df032ffb13a3d415b216a890a1304a

Transactions (4)

Coinbase46ee43ff6b8cca…731cf80cc158e2

1 in → 23 out10.0300 XPM845 B

AGFAJ5YL…ZEnBbk6G AbtgNzNb…9Atvu81w AXydriH2…RUoBRJjB AKsEVe75…B9kSuyqm AJiNZZJs…BiqAhyiP

202179219d092e…e829baece2bea6

1 in → 2 out4.1674 XPM226 B

Abv8pzf1…t4zPXDTV AY93AtBc…HoG8pHZd

eaa7b5eda93f61…848cffb6767b8b

1 in → 2 out2.7492 XPM227 B

ASVbSs25…VQ8x4GR5 AY3j6efJ…ED3ui6ZN

a8a15ca4d96eff…55e484d8cbb008

2 in → 2 out2.3536 XPM374 B

Ab3dSvM7…Qoxxb9tp AKSwUiAV…qhLx4V1w

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.

3.413 × 10⁹⁶(97-digit number)

34133903528277228067…00582321248908810999

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

3.413 × 10⁹⁶(97-digit number)

34133903528277228067…00582321248908810999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.413 × 10⁹⁶(97-digit number)

34133903528277228067…00582321248908811001

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

6.826 × 10⁹⁶(97-digit number)

68267807056554456134…01164642497817621999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.826 × 10⁹⁶(97-digit number)

68267807056554456134…01164642497817622001

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

1.365 × 10⁹⁷(98-digit number)

13653561411310891226…02329284995635243999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.365 × 10⁹⁷(98-digit number)

13653561411310891226…02329284995635244001

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

2.730 × 10⁹⁷(98-digit number)

27307122822621782453…04658569991270487999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.730 × 10⁹⁷(98-digit number)

27307122822621782453…04658569991270488001

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

5.461 × 10⁹⁷(98-digit number)

54614245645243564907…09317139982540975999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.461 × 10⁹⁷(98-digit number)

54614245645243564907…09317139982540976001

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 #282,397

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