Block #278,870

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 3:46:18 AM · Difficulty 9.9701 · 6,520,026 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c8a8c5b7112943bfe37e807bade9ece5fd577e3a68b083af8c7fff16e0a98ce4

View on Chainz ↗

Height

#278,870

Difficulty

9.970119

Transactions

Size

1.03 KB

Version

Bits

09f859b4

Nonce

18,195

Timestamp

11/28/2013, 3:46:18 AM

Confirmations

6,520,026

Mined by

⛏️ P2SHAcNCnHU9D3JiUNWyee7VjHou7ZnWtjkYN2

Merkle Root

0969f0cb6b8080b95c3176f9c43e5e73c299f0d9f3aa21066be57684f9f2d48e

Transactions (2)

Coinbasea80b6bea7c0225…f9ebc9a14cf6cc

1 in → 1 out10.0500 XPM109 B

AcNCnHU9…nWtjkYN2

be52aa2b74d9bb…680bccb928cd20

5 in → 3 out518.7704 XPM852 B

AdJ94RFC…gpZowzjd AXgUhqMn…LGh9Bksz AUwW5r2C…S26Yv51Z

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.

1.245 × 10⁹⁵(96-digit number)

12457130202560870922…31603598703603017979

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

1.245 × 10⁹⁵(96-digit number)

12457130202560870922…31603598703603017979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.245 × 10⁹⁵(96-digit number)

12457130202560870922…31603598703603017981

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

2.491 × 10⁹⁵(96-digit number)

24914260405121741844…63207197407206035959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.491 × 10⁹⁵(96-digit number)

24914260405121741844…63207197407206035961

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

4.982 × 10⁹⁵(96-digit number)

49828520810243483689…26414394814412071919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.982 × 10⁹⁵(96-digit number)

49828520810243483689…26414394814412071921

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

9.965 × 10⁹⁵(96-digit number)

99657041620486967378…52828789628824143839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.965 × 10⁹⁵(96-digit number)

99657041620486967378…52828789628824143841

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

1.993 × 10⁹⁶(97-digit number)

19931408324097393475…05657579257648287679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.993 × 10⁹⁶(97-digit number)

19931408324097393475…05657579257648287681

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