Block #227,717

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/26/2013, 1:22:14 AM · Difficulty 9.9371 · 6,569,168 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

444ab8943475d8944ba820d14176be3373df5d94e22d81c7963764034657a9a2

View on Chainz ↗

Height

#227,717

Difficulty

9.937133

Transactions

Size

617 B

Version

Bits

09efe7f7

Nonce

77,924

Timestamp

10/26/2013, 1:22:14 AM

Confirmations

6,569,168

Mined by

⛏️ P2SHATiv11uPfxAhfqFAPAcc3PrdgRbHzSGHVV

Merkle Root

9654a301a7fe4b4afce39cc1f782edf970cb6864d500b10c48998f13fe9f5437

Transactions (3)

Coinbasee823a6e3cc1892…6e5137935d935e

1 in → 1 out10.1300 XPM109 B

ATiv11uP…bHzSGHVV

c0307614a5bda5…86235fa01600d0

1 in → 2 out10.1300 XPM192 B

AQAvQSWZ…C9mFkvux AMH65TZx…hTzSL47Y

2de3e5fb93f5d1…6971078e61b53c

1 in → 2 out8.0802 XPM225 B

AXSFPdKY…6X17ePVF AYdVHCVT…uBUimwAG

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.

1.889 × 10⁹⁶(97-digit number)

18896978841474101717…46855469531992826239

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

1.889 × 10⁹⁶(97-digit number)

18896978841474101717…46855469531992826239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.889 × 10⁹⁶(97-digit number)

18896978841474101717…46855469531992826241

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

3.779 × 10⁹⁶(97-digit number)

37793957682948203435…93710939063985652479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.779 × 10⁹⁶(97-digit number)

37793957682948203435…93710939063985652481

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

7.558 × 10⁹⁶(97-digit number)

75587915365896406870…87421878127971304959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.558 × 10⁹⁶(97-digit number)

75587915365896406870…87421878127971304961

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

1.511 × 10⁹⁷(98-digit number)

15117583073179281374…74843756255942609919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.511 × 10⁹⁷(98-digit number)

15117583073179281374…74843756255942609921

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

3.023 × 10⁹⁷(98-digit number)

30235166146358562748…49687512511885219839

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