Block #446,572

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2014, 4:11:06 PM · Difficulty 10.3596 · 6,364,367 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ee88d1cd91cf165bc3e6980f2043ef6b32cd69bd9c74661aa44eef40a9d6aab6

View on Chainz ↗

Height

#446,572

Difficulty

10.359569

Transactions

Size

1.14 KB

Version

Bits

0a5c0cb4

Nonce

63,549

Timestamp

3/16/2014, 4:11:06 PM

Confirmations

6,364,367

Mined by

⛏️ laS%AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

a2125c7a5fd735060cd38eb1d59d16d5efdf41a23362fafa3ac32252b1b0669f

Transactions (2)

Coinbaseec5614683cb91a…aa01629d54aa39

1 in → 24 out9.3000 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

5602caaa489e27…432cdf87b88cf2

1 in → 1 out1.9900 XPM191 B

ASvz3ACB…qBYrswd5

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.

2.965 × 10¹⁰¹(102-digit number)

29652730020123970132…90852201515973722239

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

2.965 × 10¹⁰¹(102-digit number)

29652730020123970132…90852201515973722239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.965 × 10¹⁰¹(102-digit number)

29652730020123970132…90852201515973722241

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

5.930 × 10¹⁰¹(102-digit number)

59305460040247940264…81704403031947444479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.930 × 10¹⁰¹(102-digit number)

59305460040247940264…81704403031947444481

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

1.186 × 10¹⁰²(103-digit number)

11861092008049588052…63408806063894888959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.186 × 10¹⁰²(103-digit number)

11861092008049588052…63408806063894888961

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

2.372 × 10¹⁰²(103-digit number)

23722184016099176105…26817612127789777919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.372 × 10¹⁰²(103-digit number)

23722184016099176105…26817612127789777921

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

4.744 × 10¹⁰²(103-digit number)

47444368032198352211…53635224255579555839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.744 × 10¹⁰²(103-digit number)

47444368032198352211…53635224255579555841

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 #446,572

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