Block #479,682

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 8:12:44 PM · Difficulty 10.5099 · 6,334,658 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2f27558f3da4edbe04545b1c9f1b615f5a444ec5262e83ee3b26542ba523e1f

View on Chainz ↗

Height

#479,682

Difficulty

10.509937

Transactions

Size

884 B

Version

Bits

0a828b3a

Nonce

180,489,513

Timestamp

4/7/2014, 8:12:44 PM

Confirmations

6,334,658

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f305497e07ac9af478e35300449da0378520074d41602a83c10353bd952524a5

Transactions (4)

Coinbasec2ed4341138a53…866e0a9ef41008

1 in → 1 out9.0700 XPM116 B

AbwWkWZt…kawDhufa

33e1a6b79f4554…d3caed48008fc4

1 in → 2 out6.5653 XPM226 B

AcMNnCDo…btimwL4a AeJHfBBN…6HaQ7Pe3

204578efa29a17…5eeabd921b7869

1 in → 2 out2.7412 XPM225 B

Aaffr4EL…bJQCxKCY AGYqZcgR…cP8F8tfZ

95ca2fed60e696…ff74506d6002f8

1 in → 2 out4.5445 XPM226 B

ATCZ3P9S…3kLQR7Tz Ac24WwPt…BSeTbxUj

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.

1.647 × 10⁹⁸(99-digit number)

16476667028386212128…13058254470401409519

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

1.647 × 10⁹⁸(99-digit number)

16476667028386212128…13058254470401409519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.647 × 10⁹⁸(99-digit number)

16476667028386212128…13058254470401409521

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

3.295 × 10⁹⁸(99-digit number)

32953334056772424257…26116508940802819039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.295 × 10⁹⁸(99-digit number)

32953334056772424257…26116508940802819041

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

6.590 × 10⁹⁸(99-digit number)

65906668113544848514…52233017881605638079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.590 × 10⁹⁸(99-digit number)

65906668113544848514…52233017881605638081

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

1.318 × 10⁹⁹(100-digit number)

13181333622708969702…04466035763211276159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.318 × 10⁹⁹(100-digit number)

13181333622708969702…04466035763211276161

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

2.636 × 10⁹⁹(100-digit number)

26362667245417939405…08932071526422552319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.636 × 10⁹⁹(100-digit number)

26362667245417939405…08932071526422552321

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 #479,682

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