Block #229,110

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/26/2013, 11:34:16 PM · Difficulty 9.9379 · 6,574,496 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5518903a7a6a73a6272e61926f2198f8480ecd0a9a24d9feda3726cc065a4ec9

View on Chainz ↗

Height

#229,110

Difficulty

9.937929

Transactions

Size

650 B

Version

Bits

09f01c1d

Nonce

5,276

Timestamp

10/26/2013, 11:34:16 PM

Confirmations

6,574,496

Mined by

⛏️ P2SHAcU7DMWfgrvzpF5x7X1mU29XaiHi5xaoEi

Merkle Root

bd379ea1189f6689bb69bc38ca9accce9f18c50e781a5410319429af125ca06e

Transactions (3)

Coinbasebc20045165f704…afca132191dc30

1 in → 1 out10.1300 XPM109 B

AcU7DMWf…Hi5xaoEi

12a21c08175947…fc9c6af9e8dbaa

1 in → 2 out10.1000 XPM226 B

ASWKH6H8…MzbQCt9J AGCmTSw4…QNSsCSPC

746633de36d521…45cc34db797b8b

1 in → 2 out6.0177 XPM226 B

AHt64Csi…htp7xtE1 AVYA5FSq…eeZm8KGY

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.

2.646 × 10⁹³(94-digit number)

26462905941042219232…39278462080109974739

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

2.646 × 10⁹³(94-digit number)

26462905941042219232…39278462080109974739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.646 × 10⁹³(94-digit number)

26462905941042219232…39278462080109974741

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

5.292 × 10⁹³(94-digit number)

52925811882084438465…78556924160219949479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.292 × 10⁹³(94-digit number)

52925811882084438465…78556924160219949481

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

1.058 × 10⁹⁴(95-digit number)

10585162376416887693…57113848320439898959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.058 × 10⁹⁴(95-digit number)

10585162376416887693…57113848320439898961

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

2.117 × 10⁹⁴(95-digit number)

21170324752833775386…14227696640879797919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.117 × 10⁹⁴(95-digit number)

21170324752833775386…14227696640879797921

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

4.234 × 10⁹⁴(95-digit number)

42340649505667550772…28455393281759595839

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