Block #268,047

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 7:06:32 PM · Difficulty 9.9581 · 6,524,648 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

85cf093be930f9f051d4629e2d1a3c6b264b13cadedbd9d830a329368a311240

View on Chainz ↗

Height

#268,047

Difficulty

9.958062

Transactions

Size

3.71 KB

Version

Bits

09f54389

Nonce

19,692

Timestamp

11/21/2013, 7:06:32 PM

Confirmations

6,524,648

Merkle Root

6ea05a080dc834e4cc0ba4f669bda574fc424f737d93353335779136c8bf6e79

Transactions (4)

Coinbasedcb909f2f0778e…287fdb60dede5f

1 in → 1 out10.1200 XPM110 B

AeKNrjNj…1NEq95Ta

7bbcbb44cd5f2c…61aefcecc3ede3

3 in → 2 out113.9902 XPM522 B

AddxVbsn…aiFcAbmA ATPM2yfs…AQmg5mid

756efd4b1459ee…b429af473d9349

4 in → 2 out2900.0100 XPM668 B

AX5evZmA…Pp14ZFCw AS76sLSe…c7HmQtGm

e84545ea3220d6…cc28879287f7e5

16 in → 1 out8.2087 XPM2.35 KB

AJ4PDgGV…hWMtYWiQ

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.

1.164 × 10⁹³(94-digit number)

11648479697582660533…43421944166884500159

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

1.164 × 10⁹³(94-digit number)

11648479697582660533…43421944166884500159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.164 × 10⁹³(94-digit number)

11648479697582660533…43421944166884500161

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

2.329 × 10⁹³(94-digit number)

23296959395165321067…86843888333769000319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.329 × 10⁹³(94-digit number)

23296959395165321067…86843888333769000321

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

4.659 × 10⁹³(94-digit number)

46593918790330642135…73687776667538000639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.659 × 10⁹³(94-digit number)

46593918790330642135…73687776667538000641

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

9.318 × 10⁹³(94-digit number)

93187837580661284270…47375553335076001279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.318 × 10⁹³(94-digit number)

93187837580661284270…47375553335076001281

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

1.863 × 10⁹⁴(95-digit number)

18637567516132256854…94751106670152002559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.863 × 10⁹⁴(95-digit number)

18637567516132256854…94751106670152002561

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