Block #286,660

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 11:48:37 PM · Difficulty 9.9859 · 6,512,278 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

edb941ed5dd5a8bcd3754612e30072ccd872ca58db0733f23428c697422805d9

View on Chainz ↗

Height

#286,660

Difficulty

9.985853

Transactions

Size

831 B

Version

Bits

09fc60df

Nonce

7,971

Timestamp

11/30/2013, 11:48:37 PM

Confirmations

6,512,278

Mined by

⛏️ _aRynAPvpz12Ne3y3GdSQX5xb8QzBwoNjdsxTYA

Merkle Root

7df65effa6163f0979a8447337221d5fe70eafe0196c78508af8672fe4c323cb

Transactions (1)

Coinbase7df65effa6163f…f8672fe4c323cb

1 in → 20 out10.0100 XPM743 B

APvpz12N…NjdsxTYA AUC9smBq…SAmsuxvQ Ad9pSzHt…cpJ3y2zz AQyr8Lw3…hs4nt3Pn AVFJAbfE…U1uzUfDh

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.

4.124 × 10⁹⁰(91-digit number)

41240658019028389796…19484067285336037199

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

4.124 × 10⁹⁰(91-digit number)

41240658019028389796…19484067285336037199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.124 × 10⁹⁰(91-digit number)

41240658019028389796…19484067285336037201

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

8.248 × 10⁹⁰(91-digit number)

82481316038056779592…38968134570672074399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.248 × 10⁹⁰(91-digit number)

82481316038056779592…38968134570672074401

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

1.649 × 10⁹¹(92-digit number)

16496263207611355918…77936269141344148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.649 × 10⁹¹(92-digit number)

16496263207611355918…77936269141344148801

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

3.299 × 10⁹¹(92-digit number)

32992526415222711836…55872538282688297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.299 × 10⁹¹(92-digit number)

32992526415222711836…55872538282688297601

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

6.598 × 10⁹¹(92-digit number)

65985052830445423673…11745076565376595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.598 × 10⁹¹(92-digit number)

65985052830445423673…11745076565376595201

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