Block #2,496,466

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/29/2018, 8:24:53 PM · Difficulty 10.9742 · 4,344,780 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f2dbbeadee3af80a56326ac4be9d69677bd3fff9626442c69f0c1d9afc84bc1f

View on Chainz ↗

Height

#2,496,466

Difficulty

10.974238

Transactions

Size

1.36 KB

Version

Bits

0af967a9

Nonce

208,306,387

Timestamp

1/29/2018, 8:24:53 PM

Confirmations

4,344,780

Mined by

⛏️ P2SHAYr4UMFqLMinPzFHq6Yn4w7wVTrJB9c2HP

Merkle Root

91620600759321fe32a82260992ea463c0978670925d5f92c114baa6e7d142ae

Transactions (3)

Coinbase11b2b188109ac4…38c98e319bced2

1 in → 1 out8.3200 XPM109 B

AYr4UMFq…rJB9c2HP

bd2507e488fd32…4d5bb138b5e4a7

4 in → 2 out6664.3686 XPM670 B

AVa5dYbR…j5uZYCvt ARt66m93…zQUz6Ug2

283e1dda5cd6aa…c8cfd3a1df63e0

3 in → 2 out29.5999 XPM520 B

ATDsfC7t…6yuCP9pe Aer2kr7Y…zJGhqxFu

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.

1.853 × 10⁹⁸(99-digit number)

18532465158223954049…70551432259267829759

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

1.853 × 10⁹⁸(99-digit number)

18532465158223954049…70551432259267829759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.853 × 10⁹⁸(99-digit number)

18532465158223954049…70551432259267829761

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

3.706 × 10⁹⁸(99-digit number)

37064930316447908098…41102864518535659519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.706 × 10⁹⁸(99-digit number)

37064930316447908098…41102864518535659521

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

7.412 × 10⁹⁸(99-digit number)

74129860632895816196…82205729037071319039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.412 × 10⁹⁸(99-digit number)

74129860632895816196…82205729037071319041

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

1.482 × 10⁹⁹(100-digit number)

14825972126579163239…64411458074142638079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.482 × 10⁹⁹(100-digit number)

14825972126579163239…64411458074142638081

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

2.965 × 10⁹⁹(100-digit number)

29651944253158326478…28822916148285276159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.965 × 10⁹⁹(100-digit number)

29651944253158326478…28822916148285276161

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

5.930 × 10⁹⁹(100-digit number)

59303888506316652956…57645832296570552319

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 #2,496,466

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