Block #172,227

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/20/2013, 2:13:52 AM · Difficulty 9.8629 · 6,635,835 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dc010ff2dde30aa7c07881f8e845284820af336c790edab33271643229d6e2ed

View on Chainz ↗

Height

#172,227

Difficulty

9.862935

Transactions

Size

650 B

Version

Bits

09dce950

Nonce

249,823

Timestamp

9/20/2013, 2:13:52 AM

Confirmations

6,635,835

Mined by

⛏️ P2SHAHiscA3WFz9dnGf3xRFCFqJkKatvPD5RmV

Merkle Root

22796fab789618caa3ee1c7159fba59322ad015dc7cd16970408a7e2138967ca

Transactions (3)

Coinbase4c745bd17d0a80…c405f61fefbba1

1 in → 1 out10.2800 XPM109 B

AHiscA3W…tvPD5RmV

86437f731cc1b1…e3ffc47eadde59

1 in → 2 out4.1639 XPM226 B

ASnSjgQg…fewAaNPL AcL9ouSC…1aSS6T3j

8503e38091d099…5cb12e1ff6573b

1 in → 2 out2.0806 XPM226 B

ARs1Tjjn…ufdce1iZ AYBs9UTC…odqRGSpW

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.

2.886 × 10⁹³(94-digit number)

28869140606575101194…41387621086410552319

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

2.886 × 10⁹³(94-digit number)

28869140606575101194…41387621086410552319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.886 × 10⁹³(94-digit number)

28869140606575101194…41387621086410552321

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

5.773 × 10⁹³(94-digit number)

57738281213150202388…82775242172821104639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.773 × 10⁹³(94-digit number)

57738281213150202388…82775242172821104641

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

1.154 × 10⁹⁴(95-digit number)

11547656242630040477…65550484345642209279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.154 × 10⁹⁴(95-digit number)

11547656242630040477…65550484345642209281

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

2.309 × 10⁹⁴(95-digit number)

23095312485260080955…31100968691284418559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.309 × 10⁹⁴(95-digit number)

23095312485260080955…31100968691284418561

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

4.619 × 10⁹⁴(95-digit number)

46190624970520161910…62201937382568837119

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 #172,227

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