Block #202,230

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/10/2013, 2:31:05 AM · Difficulty 9.8946 · 6,605,886 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a50fa149db5f8d9b9a0b3baf3ab2ecec5ec2cc08dd494a537a9beacfd13f2b18

View on Chainz ↗

Height

#202,230

Difficulty

9.894596

Transactions

Size

6.58 KB

Version

Bits

09e5043e

Nonce

42,001

Timestamp

10/10/2013, 2:31:05 AM

Confirmations

6,605,886

Mined by

⛏️ P2SHAK7kWkL4sngiZYayFhX74gnWY2GHfWFBHC

Merkle Root

a5aa8960de044b45ed8c7cffd53ef488fbba554e828f6c4bc18738f9f1b64047

Transactions (4)

Coinbase4a33d33c6cb0dc…236dfdfa2e6d35

1 in → 1 out10.2800 XPM109 B

AK7kWkL4…GHfWFBHC

2b575c9fbca5c3…63f9af7cd0c83f

49 in → 2 out503.6158 XPM5.53 KB

AGwiWWWK…ipRzJ5ce ARPU9skP…DoRVGg3C

ed0be269bcb483…4ba7e2759c266e

5 in → 2 out41.0400 XPM683 B

AJLAVAcZ…tMRos59d AZiZ3BSK…ouABkYiL

63845bb0917470…bea84021765cba

1 in → 2 out10.2200 XPM191 B

Ab34XSGu…EoMuDfPR AFz9fXym…wh4UqpkL

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.

2.681 × 10⁹¹(92-digit number)

26819560678904712366…86843654812862761919

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

2.681 × 10⁹¹(92-digit number)

26819560678904712366…86843654812862761919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.681 × 10⁹¹(92-digit number)

26819560678904712366…86843654812862761921

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

5.363 × 10⁹¹(92-digit number)

53639121357809424732…73687309625725523839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.363 × 10⁹¹(92-digit number)

53639121357809424732…73687309625725523841

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

1.072 × 10⁹²(93-digit number)

10727824271561884946…47374619251451047679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.072 × 10⁹²(93-digit number)

10727824271561884946…47374619251451047681

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

2.145 × 10⁹²(93-digit number)

21455648543123769892…94749238502902095359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.145 × 10⁹²(93-digit number)

21455648543123769892…94749238502902095361

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

4.291 × 10⁹²(93-digit number)

42911297086247539785…89498477005804190719

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

Block #202,230

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