Block #225,396

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/24/2013, 11:03:56 AM · Difficulty 9.9368 · 6,569,931 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f80ef43fb4708d3a00047933e7ac465d29022a7c631c0ee4d5320242ca3acd30

View on Chainz ↗

Height

#225,396

Difficulty

9.936786

Transactions

Size

99.88 KB

Version

Bits

09efd12e

Nonce

5,290

Timestamp

10/24/2013, 11:03:56 AM

Confirmations

6,569,931

Mined by

⛏️ P2SHAX2k3g5sBwvQvbbWtJsNwtUEYQQwBtRfhf

Merkle Root

4b5ea1e1c240918b47c1158fc174c7eab2a213fc0798a452349650160c59e2df

Transactions (5)

Coinbase567c2537ba2d8e…cd05665cad58fa

1 in → 1 out11.1700 XPM109 B

AX2k3g5s…QwBtRfhf

3e9f09b4cd1c17…4eae206d7e7233

26 in → 2 out346.3840 XPM3.83 KB

AUh98hSA…ZLXK8Eh6 AN45xKJb…jzPnBV6L

bce12edd671075…a3649856509702

328 in → 2 out100.0100 XPM47.48 KB

ALZsdbkH…QGup79e2 ALG7hNHE…GVtmhodq

4c696d1a907090…bf97e34bf15776

1 in → 2 out8.0898 XPM226 B

Ab3dSvM7…Qoxxb9tp AYF6J7NN…tNs3uqhw

9f19aa9422fff9…0854a00e989865

333 in → 1 out72.9662 XPM48.16 KB

ALG7hNHE…GVtmhodq

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.

5.505 × 10⁹⁴(95-digit number)

55056382835211620668…24991221212664558079

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

5.505 × 10⁹⁴(95-digit number)

55056382835211620668…24991221212664558079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.505 × 10⁹⁴(95-digit number)

55056382835211620668…24991221212664558081

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

1.101 × 10⁹⁵(96-digit number)

11011276567042324133…49982442425329116159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.101 × 10⁹⁵(96-digit number)

11011276567042324133…49982442425329116161

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

2.202 × 10⁹⁵(96-digit number)

22022553134084648267…99964884850658232319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.202 × 10⁹⁵(96-digit number)

22022553134084648267…99964884850658232321

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

4.404 × 10⁹⁵(96-digit number)

44045106268169296534…99929769701316464639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.404 × 10⁹⁵(96-digit number)

44045106268169296534…99929769701316464641

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

8.809 × 10⁹⁵(96-digit number)

88090212536338593069…99859539402632929279

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