Block #275,481

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 5:37:05 PM · Difficulty 9.9609 · 6,520,061 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf1f035403fba2232f11f7088bc2acd968bea0d262dad8d4f5777fa5ea05205c

View on Chainz ↗

Height

#275,481

Difficulty

9.960881

Transactions

Size

8.80 KB

Version

Bits

09f5fc4e

Nonce

12,422

Timestamp

11/26/2013, 5:37:05 PM

Confirmations

6,520,061

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

6fef251972150ae2879bfffaf93db650fc290c907ea22c5d5b62cfd4da14c922

Transactions (4)

Coinbase6aaa1006c592cc…c6000a293244ec

1 in → 1 out10.1700 XPM110 B

AeKNrjNj…1NEq95Ta

ad1bc2c8f93592…48cf297fb24e8a

2 in → 3 out317.6700 XPM408 B

ANuWmJhC…rYujxJ5d AeWhPGME…DokmbLpC ALV4uf1D…S9c2E7xf

270180ba9304c5…827681422c25ea

55 in → 2 out536.8882 XPM8.02 KB

AWRrLcuF…xXpsJ4Xk APpwXKD4…x5H8Enm6

4c340882dfa264…34b8e6169fb579

1 in → 1 out1.9900 XPM192 B

ANUWTGTc…83e9DSRC

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.

2.032 × 10⁹⁶(97-digit number)

20327671181419935937…09821068008590503999

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

2.032 × 10⁹⁶(97-digit number)

20327671181419935937…09821068008590503999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.032 × 10⁹⁶(97-digit number)

20327671181419935937…09821068008590504001

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

4.065 × 10⁹⁶(97-digit number)

40655342362839871874…19642136017181007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.065 × 10⁹⁶(97-digit number)

40655342362839871874…19642136017181008001

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

8.131 × 10⁹⁶(97-digit number)

81310684725679743749…39284272034362015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.131 × 10⁹⁶(97-digit number)

81310684725679743749…39284272034362016001

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

1.626 × 10⁹⁷(98-digit number)

16262136945135948749…78568544068724031999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.626 × 10⁹⁷(98-digit number)

16262136945135948749…78568544068724032001

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

3.252 × 10⁹⁷(98-digit number)

32524273890271897499…57137088137448063999

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