Block #478,179

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 10:09:05 PM · Difficulty 10.4914 · 6,332,953 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

600da43dc80bfd7841b8b6eceb86ddbda38507d7b9de94b8a66cf4603998856f

View on Chainz ↗

Height

#478,179

Difficulty

10.491429

Transactions

Size

1.01 KB

Version

Bits

0a7dce47

Nonce

219,075,145

Timestamp

4/6/2014, 10:09:05 PM

Confirmations

6,332,953

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

fb71ac3459b7ef3786b182f70c3e2f344570463973535b763675ac367b71f01b

Transactions (4)

Coinbase9e3e163924c219…7d52ef4178c26f

1 in → 1 out9.1000 XPM116 B

AbwWkWZt…kawDhufa

3b09398e813595…4d1bd04e921470

2 in → 2 out11.7596 XPM373 B

ANGGiEoD…MWveqicP AJJu16ii…1zZTWnqc

bc945b4848775e…dd669bf644e3f6

1 in → 2 out5.0633 XPM226 B

AQDJjfLW…zyJYEbMR AXUavLHG…c4pfQuCq

14d872a60866d7…bba1498ace692b

1 in → 2 out5.7410 XPM225 B

AJdSskrD…mKiHyKTF ANZUxYNW…P1pZfYxg

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.

4.707 × 10⁹⁷(98-digit number)

47074147633465265339…12896394745526513919

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

4.707 × 10⁹⁷(98-digit number)

47074147633465265339…12896394745526513919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.707 × 10⁹⁷(98-digit number)

47074147633465265339…12896394745526513921

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

9.414 × 10⁹⁷(98-digit number)

94148295266930530679…25792789491053027839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.414 × 10⁹⁷(98-digit number)

94148295266930530679…25792789491053027841

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

1.882 × 10⁹⁸(99-digit number)

18829659053386106135…51585578982106055679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.882 × 10⁹⁸(99-digit number)

18829659053386106135…51585578982106055681

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

3.765 × 10⁹⁸(99-digit number)

37659318106772212271…03171157964212111359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.765 × 10⁹⁸(99-digit number)

37659318106772212271…03171157964212111361

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

7.531 × 10⁹⁸(99-digit number)

75318636213544424543…06342315928424222719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.531 × 10⁹⁸(99-digit number)

75318636213544424543…06342315928424222721

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 #478,179

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