Block #286,860

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 1:49:48 AM · Difficulty 9.9861 · 6,508,764 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e34498c4321498ad527199059187592dfc51caf5d67785a0f737f7caed196a1e

View on Chainz ↗

Height

#286,860

Difficulty

9.986085

Transactions

Size

1.15 KB

Version

Bits

09fc700f

Nonce

2,540

Timestamp

12/1/2013, 1:49:48 AM

Confirmations

6,508,764

Mined by

⛏️ `aR@AQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

8afa287494cc82362920f851eea873403d226f8387ae5b571a7246c0112b0d5a

Transactions (1)

Coinbase8afa287494cc82…7246c0112b0d5a

1 in → 30 out9.9900 XPM1.06 KB

AQwRN8bE…V8PsTcY9 AWGQhzDN…RDYvugUy AGFAJ5YL…ZEnBbk6G AZ2pPuKg…95SN2Yr7 AQM6XBhf…Wk2pUBmp

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.

1.332 × 10⁹⁵(96-digit number)

13320910399233720949…76783127419931642229

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

1.332 × 10⁹⁵(96-digit number)

13320910399233720949…76783127419931642229

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.332 × 10⁹⁵(96-digit number)

13320910399233720949…76783127419931642231

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

2.664 × 10⁹⁵(96-digit number)

26641820798467441899…53566254839863284459

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.664 × 10⁹⁵(96-digit number)

26641820798467441899…53566254839863284461

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

5.328 × 10⁹⁵(96-digit number)

53283641596934883799…07132509679726568919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.328 × 10⁹⁵(96-digit number)

53283641596934883799…07132509679726568921

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

1.065 × 10⁹⁶(97-digit number)

10656728319386976759…14265019359453137839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.065 × 10⁹⁶(97-digit number)

10656728319386976759…14265019359453137841

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

2.131 × 10⁹⁶(97-digit number)

21313456638773953519…28530038718906275679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.131 × 10⁹⁶(97-digit number)

21313456638773953519…28530038718906275681

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