Block #235,186

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/30/2013, 6:46:54 PM · Difficulty 9.9452 · 6,579,666 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

04c56c181583c6b49630499148db2a04b62fe71e4477fbace401e94cc0821037

View on Chainz ↗

Height

#235,186

Difficulty

9.945238

Transactions

Size

719 B

Version

Bits

09f1fb1b

Nonce

44,178

Timestamp

10/30/2013, 6:46:54 PM

Confirmations

6,579,666

Mined by

⛏️ P2SHAM1A9CZLPnH51axL7hPRTWjkm6as4Lpogj

Merkle Root

071923f22a9715740ef727efb313dee6a4bdcee0e80cee9133bcf539c15419f6

Transactions (2)

Coinbase5f52200dd55f87…00786edc2ed224

1 in → 1 out10.1100 XPM109 B

AM1A9CZL…as4Lpogj

9ec8e61099775f…856107eaa8bac1

3 in → 2 out26.2198 XPM522 B

AZVEnwMh…ThBidhNA AN7ZnJS4…uHpiPac9

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.

1.572 × 10⁸⁹(90-digit number)

15725988265787835599…73148735935988895919

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

1.572 × 10⁸⁹(90-digit number)

15725988265787835599…73148735935988895919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.572 × 10⁸⁹(90-digit number)

15725988265787835599…73148735935988895921

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

3.145 × 10⁸⁹(90-digit number)

31451976531575671198…46297471871977791839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.145 × 10⁸⁹(90-digit number)

31451976531575671198…46297471871977791841

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

6.290 × 10⁸⁹(90-digit number)

62903953063151342396…92594943743955583679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.290 × 10⁸⁹(90-digit number)

62903953063151342396…92594943743955583681

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

1.258 × 10⁹⁰(91-digit number)

12580790612630268479…85189887487911167359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.258 × 10⁹⁰(91-digit number)

12580790612630268479…85189887487911167361

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

2.516 × 10⁹⁰(91-digit number)

25161581225260536958…70379774975822334719

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 #235,186

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