Block #280,532

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 5:19:51 PM · Difficulty 9.9748 · 6,512,242 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e59fc3a2618cfe37ca44b455f3f6eea900dc144e2be9c69beb3504f3a25f2d64

View on Chainz ↗

Height

#280,532

Difficulty

9.974797

Transactions

Size

1.13 KB

Version

Bits

09f98c45

Nonce

23,426

Timestamp

11/28/2013, 5:19:51 PM

Confirmations

6,512,242

Merkle Root

389beeef002f175983e35b736d95393b972dc16fe29c28e9ee2235551ced2e2f

Transactions (2)

Coinbase4380de343e8875…a15a5e2eea3932

1 in → 1 out10.0400 XPM97 B

AYCeLhqB…eqGM6KK1

095448fe2ca247…76e29478923a78

6 in → 2 out2962.0901 XPM969 B

AbHkXKgw…ttMoijwF Aegm79px…D88sq7H1

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.

1.308 × 10⁹⁷(98-digit number)

13082242209755576975…30010415534860782079

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

1.308 × 10⁹⁷(98-digit number)

13082242209755576975…30010415534860782079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.308 × 10⁹⁷(98-digit number)

13082242209755576975…30010415534860782081

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

2.616 × 10⁹⁷(98-digit number)

26164484419511153951…60020831069721564159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.616 × 10⁹⁷(98-digit number)

26164484419511153951…60020831069721564161

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

5.232 × 10⁹⁷(98-digit number)

52328968839022307902…20041662139443128319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.232 × 10⁹⁷(98-digit number)

52328968839022307902…20041662139443128321

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

1.046 × 10⁹⁸(99-digit number)

10465793767804461580…40083324278886256639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.046 × 10⁹⁸(99-digit number)

10465793767804461580…40083324278886256641

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

2.093 × 10⁹⁸(99-digit number)

20931587535608923161…80166648557772513279

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