Block #276,680

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 7:04:10 AM · Difficulty 9.9639 · 6,514,655 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9c6cdc19ff45a3a5c6b89669fbd534ddcb50f29163697a5ae48a328700ab5b55

View on Chainz ↗

Height

#276,680

Difficulty

9.963850

Transactions

Size

121.22 KB

Version

Bits

09f6bee0

Nonce

87,063

Timestamp

11/27/2013, 7:04:10 AM

Confirmations

6,514,655

Merkle Root

bb8a1e62db6bd4eb8e5013bfd99962a9971cb2b21ac6acb706318749b194d271

Transactions (4)

Coinbase1ec8981ec18913…c3996c1045b103

1 in → 1 out11.4000 XPM110 B

AeKNrjNj…1NEq95Ta

33b95eb1d8a851…7662c6ade5b823

396 in → 1 out10.0000 XPM57.28 KB

AQGF4wCZ…FBfZNwJG

e4825dfe0a68c6…7e426f8820e316

1 in → 2 out49.9900 XPM226 B

AQGF4wCZ…FBfZNwJG AWfnhoRi…J1dsFPKU

84a99a446eb98c…afe3ec1c699db8

439 in → 2 out10.0100 XPM63.53 KB

AQGF4wCZ…FBfZNwJG ALqERwac…ARZXVbVY

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.

1.334 × 10⁹⁷(98-digit number)

13349110855318469560…42156992668304528639

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

1.334 × 10⁹⁷(98-digit number)

13349110855318469560…42156992668304528639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.334 × 10⁹⁷(98-digit number)

13349110855318469560…42156992668304528641

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

2.669 × 10⁹⁷(98-digit number)

26698221710636939120…84313985336609057279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.669 × 10⁹⁷(98-digit number)

26698221710636939120…84313985336609057281

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

5.339 × 10⁹⁷(98-digit number)

53396443421273878240…68627970673218114559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.339 × 10⁹⁷(98-digit number)

53396443421273878240…68627970673218114561

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

1.067 × 10⁹⁸(99-digit number)

10679288684254775648…37255941346436229119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.067 × 10⁹⁸(99-digit number)

10679288684254775648…37255941346436229121

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

2.135 × 10⁹⁸(99-digit number)

21358577368509551296…74511882692872458239

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