Block #2,475,114

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/16/2018, 3:36:46 AM · Difficulty 10.9637 · 4,365,303 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b33e2c71087e12f1ed2ea262aa0255699f816d506936a476be4fcf15194e89c

View on Chainz ↗

Height

#2,475,114

Difficulty

10.963745

Transactions

Size

1.36 KB

Version

Bits

0af6b800

Nonce

990,190,842

Timestamp

1/16/2018, 3:36:46 AM

Confirmations

4,365,303

Mined by

⛏️ P2SHALq9Wpt9aGpU7VN7ftMAnvyyr6vTYJ5R1Y

Merkle Root

6e218160d35dff0a03907ff2ccb70d04d80b7494b146f83d17e452ce118e4132

Transactions (3)

Coinbase7f0af79bd2c105…c4bef5895b3a96

1 in → 1 out8.3400 XPM110 B

ALq9Wpt9…vTYJ5R1Y

81d89bf014bb56…10ff660b04eccc

1 in → 2 out9750.7565 XPM227 B

AbnS1yCJ…9j6iP7rg AXwsmPPr…6VMrFrtM

0d4817c8196acf…be9e807ae0fbd1

6 in → 2 out4.0114 XPM967 B

AMjZ87GH…cvurqAXE AZvZXc4o…tbmaZmDH

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.

1.026 × 10⁹⁴(95-digit number)

10263828253871996558…04429142085273974159

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

1.026 × 10⁹⁴(95-digit number)

10263828253871996558…04429142085273974159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.026 × 10⁹⁴(95-digit number)

10263828253871996558…04429142085273974161

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

2.052 × 10⁹⁴(95-digit number)

20527656507743993116…08858284170547948319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.052 × 10⁹⁴(95-digit number)

20527656507743993116…08858284170547948321

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

4.105 × 10⁹⁴(95-digit number)

41055313015487986233…17716568341095896639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.105 × 10⁹⁴(95-digit number)

41055313015487986233…17716568341095896641

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

8.211 × 10⁹⁴(95-digit number)

82110626030975972467…35433136682191793279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.211 × 10⁹⁴(95-digit number)

82110626030975972467…35433136682191793281

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

1.642 × 10⁹⁵(96-digit number)

16422125206195194493…70866273364383586559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.642 × 10⁹⁵(96-digit number)

16422125206195194493…70866273364383586561

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,475,114

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