Block #224,765

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/24/2013, 12:21:41 AM · Difficulty 9.9369 · 6,572,119 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9f8ebcaf01baa2ed2e436f5f6c610f939e4257eab7c0083b0c3e02ee47c8da56

View on Chainz ↗

Height

#224,765

Difficulty

9.936874

Transactions

Size

12.03 KB

Version

Bits

09efd6f9

Nonce

74,196

Timestamp

10/24/2013, 12:21:41 AM

Confirmations

6,572,119

Mined by

⛏️ P2SHAW8Jvtxxe4RStEa5xdDEMx4qXsDaZn2Wtg

Merkle Root

b2e1b246f378fcb64b1d9a4f5f89f3656d3950f22059723aef0aa13c4677850a

Transactions (5)

Coinbaseacc9def1f70db2…2ec2f3edaa4393

1 in → 1 out10.2500 XPM109 B

AW8Jvtxx…DaZn2Wtg

a2e48670b96728…575ef450ad0b87

11 in → 1 out25.0000 XPM1.63 KB

AXypnjGi…mWEc3YWM

3a268b341dacac…973ce237c40977

67 in → 2 out3.6177 XPM9.76 KB

AWVGMVer…oj57pvei ARQU3dnp…BDAnYVEe

6ac200c247bfa7…0250d836330a16

1 in → 2 out6.5477 XPM225 B

AK5ah2SN…8yeFr1tD AeNZnszq…z8T2PAj4

e619afedfe66e4…ac0fc2336f725c

1 in → 2 out2.5871 XPM226 B

AaHaNnZZ…w5CtpS4F AVKwwQ8K…2LzrWe5s

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.

1.143 × 10⁹²(93-digit number)

11430766999236029009…52834432721272791319

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

1.143 × 10⁹²(93-digit number)

11430766999236029009…52834432721272791319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.143 × 10⁹²(93-digit number)

11430766999236029009…52834432721272791321

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

2.286 × 10⁹²(93-digit number)

22861533998472058018…05668865442545582639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.286 × 10⁹²(93-digit number)

22861533998472058018…05668865442545582641

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

4.572 × 10⁹²(93-digit number)

45723067996944116036…11337730885091165279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.572 × 10⁹²(93-digit number)

45723067996944116036…11337730885091165281

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

9.144 × 10⁹²(93-digit number)

91446135993888232072…22675461770182330559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.144 × 10⁹²(93-digit number)

91446135993888232072…22675461770182330561

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

1.828 × 10⁹³(94-digit number)

18289227198777646414…45350923540364661119

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