Block #283,755

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 9:01:45 PM · Difficulty 9.9816 · 6,521,956 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67475998b6b99cfc00d381e3ec53e73400c07ca74226e9f79535b140c76706e3

View on Chainz ↗

Height

#283,755

Difficulty

9.981596

Transactions

Size

548 B

Version

Bits

09fb49e2

Nonce

133,241

Timestamp

11/29/2013, 9:01:45 PM

Confirmations

6,521,956

Mined by

⛏️ P2SHAczziGoaec4RPgvrGcUwYWvRLHdsHNtnSo

Merkle Root

a71a7f6943844bcba63108ff06637ca9ec0087dd87c5a9c23d52cbb53b40bdcc

Transactions (3)

Coinbase70211b806d5f3a…b00d2d8a0bef64

1 in → 1 out10.0400 XPM109 B

AczziGoa…dsHNtnSo

73dfb283b87d7f…8602602aab03e7

1 in → 1 out10.0300 XPM158 B

AUQWNLX2…FxwsS5kV

70effdaf326e25…2c236d3e249056

1 in → 1 out15.0800 XPM191 B

AVCNCEbZ…W12d36Rj

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.

1.818 × 10⁹⁵(96-digit number)

18185683255719538480…55923105832205323519

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

1.818 × 10⁹⁵(96-digit number)

18185683255719538480…55923105832205323519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.818 × 10⁹⁵(96-digit number)

18185683255719538480…55923105832205323521

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

3.637 × 10⁹⁵(96-digit number)

36371366511439076961…11846211664410647039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.637 × 10⁹⁵(96-digit number)

36371366511439076961…11846211664410647041

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

7.274 × 10⁹⁵(96-digit number)

72742733022878153923…23692423328821294079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.274 × 10⁹⁵(96-digit number)

72742733022878153923…23692423328821294081

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

1.454 × 10⁹⁶(97-digit number)

14548546604575630784…47384846657642588159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.454 × 10⁹⁶(97-digit number)

14548546604575630784…47384846657642588161

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

2.909 × 10⁹⁶(97-digit number)

29097093209151261569…94769693315285176319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.909 × 10⁹⁶(97-digit number)

29097093209151261569…94769693315285176321

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