Block #416,817

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2014, 4:42:33 PM · Difficulty 10.3995 · 6,392,835 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

32e3a7634b4976bba57bb7963ab9823b7d11369c60d600a5118c4a76b642f491

View on Chainz ↗

Height

#416,817

Difficulty

10.399496

Transactions

Size

935 B

Version

Bits

0a664557

Nonce

179,905

Timestamp

2/23/2014, 4:42:33 PM

Confirmations

6,392,835

Mined by

⛏️ 1\aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ec705824cac119855f39c7a6f1cc318e92f191593129de0a309c0625a11086f9

Transactions (1)

Coinbaseec705824cac119…9c0625a11086f9

1 in → 23 out9.2300 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AdpFCT3a…iEK8FuLE

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.

3.653 × 10⁹⁵(96-digit number)

36534576287816253965…40423170031594881279

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

3.653 × 10⁹⁵(96-digit number)

36534576287816253965…40423170031594881279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.653 × 10⁹⁵(96-digit number)

36534576287816253965…40423170031594881281

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

7.306 × 10⁹⁵(96-digit number)

73069152575632507930…80846340063189762559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.306 × 10⁹⁵(96-digit number)

73069152575632507930…80846340063189762561

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

1.461 × 10⁹⁶(97-digit number)

14613830515126501586…61692680126379525119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.461 × 10⁹⁶(97-digit number)

14613830515126501586…61692680126379525121

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

2.922 × 10⁹⁶(97-digit number)

29227661030253003172…23385360252759050239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.922 × 10⁹⁶(97-digit number)

29227661030253003172…23385360252759050241

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

5.845 × 10⁹⁶(97-digit number)

58455322060506006344…46770720505518100479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.845 × 10⁹⁶(97-digit number)

58455322060506006344…46770720505518100481

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 #416,817

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