Block #2,478,096

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2018, 1:55:28 AM · Difficulty 10.9652 · 4,354,488 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0fecc7db02be944c743735d59a1879692a6a7d681290f70caf869053be3ff8c1

View on Chainz ↗

Height

#2,478,096

Difficulty

10.965242

Transactions

Size

1.79 KB

Version

Bits

0af71a15

Nonce

561,558,183

Timestamp

1/18/2018, 1:55:28 AM

Confirmations

4,354,488

Mined by

⛏️ P2SHAQqvQ7wTcegE5oTTbohrx5XykCAD5g8bp7

Merkle Root

58f9ac005b8d87dc29188c20031a8644c9ce80e1c515d79ad59c95bd4f8a7617

Transactions (3)

Coinbase1e004e286ff74c…150f9d0da0409f

1 in → 1 out8.3300 XPM109 B

AQqvQ7wT…AD5g8bp7

fba5fdd601b77d…742b5ab2793ca7

6 in → 2 out300.0105 XPM968 B

ANf36S48…2hyNz87d AXHFCHoJ…Y33z9utB

543b84d8f39f15…ba4e70af23ac82

4 in → 2 out51.0483 XPM669 B

AT3AUtP9…Q28XYKdp AMHwTpTF…whtMuMAb

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.

6.746 × 10⁹³(94-digit number)

67467992356451711415…22989931300138013919

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

6.746 × 10⁹³(94-digit number)

67467992356451711415…22989931300138013919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.746 × 10⁹³(94-digit number)

67467992356451711415…22989931300138013921

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

1.349 × 10⁹⁴(95-digit number)

13493598471290342283…45979862600276027839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.349 × 10⁹⁴(95-digit number)

13493598471290342283…45979862600276027841

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

2.698 × 10⁹⁴(95-digit number)

26987196942580684566…91959725200552055679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.698 × 10⁹⁴(95-digit number)

26987196942580684566…91959725200552055681

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

5.397 × 10⁹⁴(95-digit number)

53974393885161369132…83919450401104111359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.397 × 10⁹⁴(95-digit number)

53974393885161369132…83919450401104111361

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

1.079 × 10⁹⁵(96-digit number)

10794878777032273826…67838900802208222719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.079 × 10⁹⁵(96-digit number)

10794878777032273826…67838900802208222721

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 #2,478,096

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