Block #26,080

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 4:15:00 AM · Difficulty 7.9737 · 6,779,891 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e5d8921ecb5d4e91c1064c3e6a2c9236c51ca952a08eef92486c716e40bf0a8a

View on Chainz ↗

Height

#26,080

Difficulty

7.973691

Transactions

Size

699 B

Version

Bits

07f943cd

Nonce

204

Timestamp

7/13/2013, 4:15:00 AM

Confirmations

6,779,891

Mined by

⛏️ P2SHAedCo1qGFPkcqJFcCvRmpjxjtczFAZ1w75

Merkle Root

07fb4509838471aaa1e834b0f28ccee034216f6163e76533420a5de73338903c

Transactions (3)

Coinbase5eaff2220d7325…cec9f377edb450

1 in → 1 out15.7300 XPM108 B

AedCo1qG…zFAZ1w75

c2598dfe2084bb…d065f24475bb68

2 in → 2 out31.7500 XPM307 B

AK6DLNgv…M4GgceQx APTnPSkD…CKDpprAw

c492deb0ef5b10…ec3980e91552b9

1 in → 2 out15.9000 XPM192 B

AN3ezWSm…BdyijYTA Aawn9XBp…AT8dv9Uf

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.

8.258 × 10⁹⁸(99-digit number)

82584167986299031057…23371118769201580119

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

8.258 × 10⁹⁸(99-digit number)

82584167986299031057…23371118769201580119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.258 × 10⁹⁸(99-digit number)

82584167986299031057…23371118769201580121

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

1.651 × 10⁹⁹(100-digit number)

16516833597259806211…46742237538403160239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.651 × 10⁹⁹(100-digit number)

16516833597259806211…46742237538403160241

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

3.303 × 10⁹⁹(100-digit number)

33033667194519612422…93484475076806320479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.303 × 10⁹⁹(100-digit number)

33033667194519612422…93484475076806320481

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

6.606 × 10⁹⁹(100-digit number)

66067334389039224845…86968950153612640959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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