Block #475,071

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/4/2014, 11:56:38 PM · Difficulty 10.4555 · 6,333,110 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb16a1556b668c3fe82fc20f531c473f9a24dcb43cf53a2f7a79cca2599c2c72

View on Chainz ↗

Height

#475,071

Difficulty

10.455487

Transactions

Size

914 B

Version

Bits

0a749acf

Nonce

111,089

Timestamp

4/4/2014, 11:56:38 PM

Confirmations

6,333,110

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

c2f45f78e793cb0b53de56c7b05d9bbfe67d4e2312c69273ad966765b4374b23

Transactions (2)

Coinbase5482769759452e…e7f8ef030c72a5

1 in → 3 out9.1400 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

59ece627f4e162…a3f41a188c973d

3 in → 9 out27.6400 XPM659 B

AH4RoQfU…FbYuDEQF AXHYt6qb…r5FS5i7c AeKNrjNj…1NEq95Ta AJJqf2Po…tRLxW6P2 AXtUqJwy…tydVS7cu

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.

5.241 × 10⁹⁵(96-digit number)

52418838575603209278…85863923165079299839

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

5.241 × 10⁹⁵(96-digit number)

52418838575603209278…85863923165079299839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.241 × 10⁹⁵(96-digit number)

52418838575603209278…85863923165079299841

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

1.048 × 10⁹⁶(97-digit number)

10483767715120641855…71727846330158599679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.048 × 10⁹⁶(97-digit number)

10483767715120641855…71727846330158599681

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

2.096 × 10⁹⁶(97-digit number)

20967535430241283711…43455692660317199359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.096 × 10⁹⁶(97-digit number)

20967535430241283711…43455692660317199361

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

4.193 × 10⁹⁶(97-digit number)

41935070860482567422…86911385320634398719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.193 × 10⁹⁶(97-digit number)

41935070860482567422…86911385320634398721

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

8.387 × 10⁹⁶(97-digit number)

83870141720965134844…73822770641268797439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.387 × 10⁹⁶(97-digit number)

83870141720965134844…73822770641268797441

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

1.677 × 10⁹⁷(98-digit number)

16774028344193026968…47645541282537594879

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 #475,071

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