Block #284,327

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 2:19:24 AM · Difficulty 9.9825 · 6,507,562 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d1e1196b3585f4ad7ee007027c730ad693a1955c3590915182c27b8e39a708f1

View on Chainz ↗

Height

#284,327

Difficulty

9.982516

Transactions

Size

1.08 KB

Version

Bits

09fb862d

Nonce

13,464

Timestamp

11/30/2013, 2:19:24 AM

Confirmations

6,507,562

Merkle Root

7cad0d3c9711d8170e57a7f10404c1143348d2dd0d13bca777d457828d81a76f

Transactions (1)

Coinbase7cad0d3c9711d8…d457828d81a76f

1 in → 28 out10.0000 XPM1014 B

AGFAJ5YL…ZEnBbk6G AdwTEXyC…NwbVbqZV AcP9aGkN…9c7TeeiQ AQAX2v64…6CKTrG2b AZ2pPuKg…95SN2Yr7

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.

8.014 × 10⁹³(94-digit number)

80147759957653999741…17117515251213364759

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

8.014 × 10⁹³(94-digit number)

80147759957653999741…17117515251213364759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.014 × 10⁹³(94-digit number)

80147759957653999741…17117515251213364761

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

1.602 × 10⁹⁴(95-digit number)

16029551991530799948…34235030502426729519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.602 × 10⁹⁴(95-digit number)

16029551991530799948…34235030502426729521

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

3.205 × 10⁹⁴(95-digit number)

32059103983061599896…68470061004853459039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.205 × 10⁹⁴(95-digit number)

32059103983061599896…68470061004853459041

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

6.411 × 10⁹⁴(95-digit number)

64118207966123199793…36940122009706918079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.411 × 10⁹⁴(95-digit number)

64118207966123199793…36940122009706918081

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

1.282 × 10⁹⁵(96-digit number)

12823641593224639958…73880244019413836159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.282 × 10⁹⁵(96-digit number)

12823641593224639958…73880244019413836161

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