Block #26,622

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 6:01:54 AM · Difficulty 7.9759 · 6,764,365 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

32dee79bf0ea97d9f0e3295e0bb2a68a113a34614b192139878814da314b0d87

View on Chainz ↗

Height

#26,622

Difficulty

7.975881

Transactions

Size

1.67 KB

Version

Bits

07f9d350

Nonce

271

Timestamp

7/13/2013, 6:01:54 AM

Confirmations

6,764,365

Merkle Root

1535d8bbda0b17be32790e5bb1a975c9eaa3ad4699db2dfda80d15ef39a2569c

Transactions (3)

Coinbased6f051ea3519da…89c670c542f731

1 in → 1 out15.7300 XPM108 B

AcEF3KBY…GgxNk4yL

b4854bc636dc9d…ff68c474ddf585

2 in → 2 out47.3800 XPM375 B

AcMMCWBM…9yuoV5ui AZtCX4LT…teQvXwUK

26f1343c24cac5…947ab954d7d03e

6 in → 7 out0.5906 XPM1.11 KB

AcWVSMpG…Smxw36B8 AZWmzskb…zcoAeLZq AUxC2GFy…qGAXVVUe AXkS7Ymv…jZ4AENA7 AH9Kgxzk…RQVVzNTY

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.

1.729 × 10⁹⁶(97-digit number)

17296850553936358296…89202005785284725749

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

1.729 × 10⁹⁶(97-digit number)

17296850553936358296…89202005785284725749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.729 × 10⁹⁶(97-digit number)

17296850553936358296…89202005785284725751

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

3.459 × 10⁹⁶(97-digit number)

34593701107872716593…78404011570569451499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.459 × 10⁹⁶(97-digit number)

34593701107872716593…78404011570569451501

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

6.918 × 10⁹⁶(97-digit number)

69187402215745433187…56808023141138902999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.918 × 10⁹⁶(97-digit number)

69187402215745433187…56808023141138903001

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

1.383 × 10⁹⁷(98-digit number)

13837480443149086637…13616046282277805999

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