Block #280,881

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 8:18:03 PM · Difficulty 9.9756 · 6,560,147 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7fc29c50de545be973163351c96290c11810f9091a838943bea3806e39dfd26e

View on Chainz ↗

Height

#280,881

Difficulty

9.975648

Transactions

Size

1.08 KB

Version

Bits

09f9c40c

Nonce

75,892

Timestamp

11/28/2013, 8:18:03 PM

Confirmations

6,560,147

Mined by

⛏️ P2SHAdwXd1Vwxx9MXwRqC5VnzVcjMuMS5q7t3v

Merkle Root

b4b031877ffd7829c6de8d91247d2546f746d282a4045d8d2acf9d0418e77af8

Transactions (5)

Coinbase937102bfe4878f…7437943caed016

1 in → 1 out10.0700 XPM109 B

AdwXd1Vw…MS5q7t3v

5260f1b46307ae…32b9cafa5632e9

1 in → 2 out3.2902 XPM226 B

AYNitiKx…PFGZ6ohD AJ4vM4gg…PHXhnqzQ

a4944472b09124…86a8ec696a1fc0

1 in → 2 out6.9898 XPM226 B

AKw9R6bj…311Jsgds APKr4amp…XEn6M7KM

489aff302742f9…eae3bee4895216

1 in → 2 out4.9320 XPM225 B

ATV6bnUx…fbPDF9Mk AYgHJyyK…jKL1M6A5

7caa9cbf30a395…f3c5ea023da6eb

1 in → 2 out3.8559 XPM226 B

AGQxR1oS…2N1xAZXN AHtC1unt…FKCWu4wC

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.

5.161 × 10⁹¹(92-digit number)

51613228696581133390…19361211414546699599

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

5.161 × 10⁹¹(92-digit number)

51613228696581133390…19361211414546699599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.161 × 10⁹¹(92-digit number)

51613228696581133390…19361211414546699601

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

1.032 × 10⁹²(93-digit number)

10322645739316226678…38722422829093399199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.032 × 10⁹²(93-digit number)

10322645739316226678…38722422829093399201

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

2.064 × 10⁹²(93-digit number)

20645291478632453356…77444845658186798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.064 × 10⁹²(93-digit number)

20645291478632453356…77444845658186798401

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

4.129 × 10⁹²(93-digit number)

41290582957264906712…54889691316373596799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.129 × 10⁹²(93-digit number)

41290582957264906712…54889691316373596801

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

8.258 × 10⁹²(93-digit number)

82581165914529813424…09779382632747193599

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 #280,881

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