Block #285,830

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 3:47:00 PM · Difficulty 9.9848 · 6,520,203 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

887dcb71ed684e7f90e2cf05f45e92e93193baa803b42c8cf56c9e26e1b7e039

View on Chainz ↗

Height

#285,830

Difficulty

9.984820

Transactions

Size

1.18 KB

Version

Bits

09fc1d25

Nonce

258,347

Timestamp

11/30/2013, 3:47:00 PM

Confirmations

6,520,203

Mined by

⛏️ \aR2AGFAJ5YLhSEKHJ6SLzkv6wy6PiZEnBbk6G

Merkle Root

1c699402d750834fb51d9f360db6bcf02a149db629e0e0ca486da72946e736c8

Transactions (1)

Coinbase1c699402d75083…6da72946e736c8

1 in → 31 out10.0000 XPM1.09 KB

AGFAJ5YL…ZEnBbk6G Ad9pSzHt…cpJ3y2zz APeshfYV…3PKcKMKH AJHH6QuE…N3s6fxLC AVKFC9nD…J9zTymTX

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.

4.070 × 10⁹³(94-digit number)

40706682262944849169…32524655932252485999

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

4.070 × 10⁹³(94-digit number)

40706682262944849169…32524655932252485999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.070 × 10⁹³(94-digit number)

40706682262944849169…32524655932252486001

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

8.141 × 10⁹³(94-digit number)

81413364525889698339…65049311864504971999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.141 × 10⁹³(94-digit number)

81413364525889698339…65049311864504972001

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

1.628 × 10⁹⁴(95-digit number)

16282672905177939667…30098623729009943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.628 × 10⁹⁴(95-digit number)

16282672905177939667…30098623729009944001

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

3.256 × 10⁹⁴(95-digit number)

32565345810355879335…60197247458019887999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.256 × 10⁹⁴(95-digit number)

32565345810355879335…60197247458019888001

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

6.513 × 10⁹⁴(95-digit number)

65130691620711758671…20394494916039775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.513 × 10⁹⁴(95-digit number)

65130691620711758671…20394494916039776001

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