Block #282,204

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 7:33:43 AM · Difficulty 9.9786 · 6,535,447 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ced109a36bac3fac8de1f0bca2f0dc1a2eb859b04f2d3ca37d8bbf9f209dad2c

View on Chainz ↗

Height

#282,204

Difficulty

9.978621

Transactions

Size

1.05 KB

Version

Bits

09fa86e7

Nonce

76,944

Timestamp

11/29/2013, 7:33:43 AM

Confirmations

6,535,447

Mined by

⛏️ \NaRCTAKEwr54iEsuosjdBu66r2F564f9BfmMkRh

Merkle Root

8d0d95b77e2a72b9a1e00c05b16b6a42dad5fe2a2995f1b91094e34a122a76ac

Transactions (1)

Coinbase8d0d95b77e2a72…94e34a122a76ac

1 in → 27 out10.0300 XPM981 B

AKEwr54i…9BfmMkRh Af5qanha…3S4JZCTK ASLqdKi2…VhTmrwFv AGFAJ5YL…ZEnBbk6G Ad9pSzHt…cpJ3y2zz

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.

1.159 × 10⁹⁵(96-digit number)

11598877076600144365…65478381242350131559

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

1.159 × 10⁹⁵(96-digit number)

11598877076600144365…65478381242350131559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.159 × 10⁹⁵(96-digit number)

11598877076600144365…65478381242350131561

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

2.319 × 10⁹⁵(96-digit number)

23197754153200288730…30956762484700263119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.319 × 10⁹⁵(96-digit number)

23197754153200288730…30956762484700263121

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

4.639 × 10⁹⁵(96-digit number)

46395508306400577460…61913524969400526239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.639 × 10⁹⁵(96-digit number)

46395508306400577460…61913524969400526241

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

9.279 × 10⁹⁵(96-digit number)

92791016612801154920…23827049938801052479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.279 × 10⁹⁵(96-digit number)

92791016612801154920…23827049938801052481

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

1.855 × 10⁹⁶(97-digit number)

18558203322560230984…47654099877602104959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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

Block #282,204

Cookie Preferences