Block #223,869

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/23/2013, 8:40:38 AM · Difficulty 9.9373 · 6,581,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

92786c9e5a2dcee5137e9938a00e09bb4a71c25f07b6862c07b2a8310664ef1b

View on Chainz ↗

Height

#223,869

Difficulty

9.937325

Transactions

Size

392 B

Version

Bits

09eff481

Nonce

9,492

Timestamp

10/23/2013, 8:40:38 AM

Confirmations

6,581,173

Mined by

⛏️ P2SHAKPv4hRSyVaQ7o17yc9G3ZiWAUVEyrR9j7

Merkle Root

2ab5c3af0070b261b1f958569c6c208a7930ad52fd4131594e241a94065d4fb8

Transactions (2)

Coinbaseb39cf9d1987c06…cb0b9436d7a900

1 in → 1 out10.1200 XPM109 B

AKPv4hRS…VEyrR9j7

90d69f1da7c489…d9d12a4b53b612

1 in → 2 out10.1500 XPM193 B

AQAvQSWZ…C9mFkvux AaC2Vjpo…YSzdQbtm

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.

2.157 × 10⁹⁵(96-digit number)

21571170335162522842…06721726761906867199

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

2.157 × 10⁹⁵(96-digit number)

21571170335162522842…06721726761906867199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.157 × 10⁹⁵(96-digit number)

21571170335162522842…06721726761906867201

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

4.314 × 10⁹⁵(96-digit number)

43142340670325045685…13443453523813734399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.314 × 10⁹⁵(96-digit number)

43142340670325045685…13443453523813734401

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

8.628 × 10⁹⁵(96-digit number)

86284681340650091370…26886907047627468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.628 × 10⁹⁵(96-digit number)

86284681340650091370…26886907047627468801

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

1.725 × 10⁹⁶(97-digit number)

17256936268130018274…53773814095254937599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.725 × 10⁹⁶(97-digit number)

17256936268130018274…53773814095254937601

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

3.451 × 10⁹⁶(97-digit number)

34513872536260036548…07547628190509875199

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