Block #277,610

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 3:39:43 PM · Difficulty 9.9667 · 6,513,332 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ff6af88b6c79306d46781bff24681b37cff5c7f181995031ed3e9be01e49244a

View on Chainz ↗

Height

#277,610

Difficulty

9.966740

Transactions

Size

1.07 KB

Version

Bits

09f77c4b

Nonce

148,282

Timestamp

11/27/2013, 3:39:43 PM

Confirmations

6,513,332

Merkle Root

12b584b974a1e51d844eb56090db5da82b7bf431ed0f3aab9421705973b64cb8

Transactions (3)

Coinbase50a99433370af2…6946aaec2c2871

1 in → 1 out10.0700 XPM110 B

AeKNrjNj…1NEq95Ta

de000b9cb6522e…485b36600ab8b7

1 in → 2 out39.9900 XPM227 B

AJHaUqo8…Pc289USe AVabuaiK…ugWeQTed

88a0c1c1e59018…3bef68f3b1d035

4 in → 2 out44.9480 XPM669 B

AcauLkKC…TKbYp6V3 AVAgkQ76…VuChqXE6

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.

6.078 × 10⁹⁶(97-digit number)

60781688016463593249…08181774755806207999

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

6.078 × 10⁹⁶(97-digit number)

60781688016463593249…08181774755806207999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.078 × 10⁹⁶(97-digit number)

60781688016463593249…08181774755806208001

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

1.215 × 10⁹⁷(98-digit number)

12156337603292718649…16363549511612415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.215 × 10⁹⁷(98-digit number)

12156337603292718649…16363549511612416001

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

2.431 × 10⁹⁷(98-digit number)

24312675206585437299…32727099023224831999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.431 × 10⁹⁷(98-digit number)

24312675206585437299…32727099023224832001

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

4.862 × 10⁹⁷(98-digit number)

48625350413170874599…65454198046449663999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.862 × 10⁹⁷(98-digit number)

48625350413170874599…65454198046449664001

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

9.725 × 10⁹⁷(98-digit number)

97250700826341749198…30908396092899327999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.725 × 10⁹⁷(98-digit number)

97250700826341749198…30908396092899328001

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