Block #224,569

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/23/2013, 8:52:25 PM · Difficulty 9.9370 · 6,568,351 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

206ffdb516dec89fe853f35856a30793bdf8a1a8290527cb97eabb7a0ae43a78

View on Chainz ↗

Height

#224,569

Difficulty

9.937041

Transactions

Size

1.48 KB

Version

Bits

09efe1ef

Nonce

120,135

Timestamp

10/23/2013, 8:52:25 PM

Confirmations

6,568,351

Merkle Root

6baf8b68e7785488f1f45578bc8fc75a64f4b6ff5cf207cabedda5ffc19cf751

Transactions (5)

Coinbase2f31367a2d6291…9188d4a7a0c1ad

1 in → 1 out10.1500 XPM109 B

ALVthvdB…rNo2Y76q

be7c52ea93c924…85e26ce43f6fbd

4 in → 2 out3.7261 XPM671 B

ANUs69re…fnQzzwER Aatiotat…g8awLdYA

5a7280dd786851…db552f1fc034a6

1 in → 2 out10.1957 XPM192 B

ANjoZavn…VrcsapZU AQAvQSWZ…C9mFkvux

b8ae934a186858…efa1a67b699996

1 in → 2 out10.1000 XPM226 B

ARskhKeb…UgDvvX9P AJqD1YKt…p7d3Pye1

55f8590f350fc3…1f669b9736ecdf

1 in → 2 out10.1000 XPM226 B

AJJkkVsK…UBjEDj4x AHzxAdBT…pXaksKA4

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.

4.089 × 10⁹²(93-digit number)

40890146226676705171…05190121951602211669

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

4.089 × 10⁹²(93-digit number)

40890146226676705171…05190121951602211669

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.089 × 10⁹²(93-digit number)

40890146226676705171…05190121951602211671

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

8.178 × 10⁹²(93-digit number)

81780292453353410343…10380243903204423339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.178 × 10⁹²(93-digit number)

81780292453353410343…10380243903204423341

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

1.635 × 10⁹³(94-digit number)

16356058490670682068…20760487806408846679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.635 × 10⁹³(94-digit number)

16356058490670682068…20760487806408846681

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

3.271 × 10⁹³(94-digit number)

32712116981341364137…41520975612817693359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.271 × 10⁹³(94-digit number)

32712116981341364137…41520975612817693361

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

6.542 × 10⁹³(94-digit number)

65424233962682728274…83041951225635386719

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