Block #2,647,142

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 6:42:14 PM · Difficulty 11.7558 · 4,183,789 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a434a57c44bf0406591ee52d7bbb413310c6b1f61ddd1a82e31f3cacc0304ead

View on Chainz ↗

Height

#2,647,142

Difficulty

11.755825

Transactions

Size

2.16 KB

Version

Bits

0bc17dc5

Nonce

1,119,181,603

Timestamp

5/3/2018, 6:42:14 PM

Confirmations

4,183,789

Mined by

⛏️ P2SHAK278sJ8aQqYpyAHs2nVX6pHFEofTUzWEz

Merkle Root

284b383f827bea4e2b05968dcc4c4b039e7eda6a6b47fe996c826400b6618e6a

Transactions (4)

Coinbase386e47ad885b9e…f0641a2f567aa5

1 in → 1 out7.2500 XPM110 B

AK278sJ8…ofTUzWEz

78782a1129d77c…89ef47d9259a9d

5 in → 2 out194.5167 XPM817 B

AMacMFhM…iFNVuut4 AFx6tt3S…4S6cnzG1

0e77f01a376c54…6882d3e432e09b

4 in → 2 out2664.8126 XPM669 B

AVa5dYbR…j5uZYCvt ALDRDTWA…iz2z2aCY

5c020a6197b39e…1d223c88d5c654

3 in → 2 out1.9764 XPM524 B

AMwBprBV…QYV3RP2y AGoiBGFT…FAKXtnWC

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.

1.780 × 10⁹⁴(95-digit number)

17809645724690151413…40585000322846483039

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

1.780 × 10⁹⁴(95-digit number)

17809645724690151413…40585000322846483039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.780 × 10⁹⁴(95-digit number)

17809645724690151413…40585000322846483041

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

3.561 × 10⁹⁴(95-digit number)

35619291449380302827…81170000645692966079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.561 × 10⁹⁴(95-digit number)

35619291449380302827…81170000645692966081

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

7.123 × 10⁹⁴(95-digit number)

71238582898760605655…62340001291385932159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.123 × 10⁹⁴(95-digit number)

71238582898760605655…62340001291385932161

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

1.424 × 10⁹⁵(96-digit number)

14247716579752121131…24680002582771864319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.424 × 10⁹⁵(96-digit number)

14247716579752121131…24680002582771864321

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

2.849 × 10⁹⁵(96-digit number)

28495433159504242262…49360005165543728639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.849 × 10⁹⁵(96-digit number)

28495433159504242262…49360005165543728641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.699 × 10⁹⁵(96-digit number)

56990866319008484524…98720010331087457279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,647,142

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