Block #432,538

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 11:33:03 PM · Difficulty 10.3413 · 6,368,053 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48176a9c4933cfcd9e3f441630f40ab13ddc632e804fa540b9236246de98ca9a

View on Chainz ↗

Height

#432,538

Difficulty

10.341311

Transactions

Size

1005 B

Version

Bits

0a576025

Nonce

155,496

Timestamp

3/6/2014, 11:33:03 PM

Confirmations

6,368,053

Mined by

⛏️ aSiARyWs1reBFo8YdEUdVyeeKr9FtQWSKjozo

Merkle Root

1502715b07d6f494f681bfdd0859a8edfb1c8cf53439dd1b87eb72e023e5d9b3

Transactions (1)

Coinbase1502715b07d6f4…eb72e023e5d9b3

1 in → 25 out9.3400 XPM913 B

ARyWs1re…QWSKjozo Aaffr4EL…bJQCxKCY Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AScAzqGc…BZ6tV1vJ

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.

1.194 × 10⁹⁹(100-digit number)

11946023628969228706…51569520035033111039

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

1.194 × 10⁹⁹(100-digit number)

11946023628969228706…51569520035033111039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.194 × 10⁹⁹(100-digit number)

11946023628969228706…51569520035033111041

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

2.389 × 10⁹⁹(100-digit number)

23892047257938457413…03139040070066222079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.389 × 10⁹⁹(100-digit number)

23892047257938457413…03139040070066222081

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

4.778 × 10⁹⁹(100-digit number)

47784094515876914827…06278080140132444159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.778 × 10⁹⁹(100-digit number)

47784094515876914827…06278080140132444161

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

9.556 × 10⁹⁹(100-digit number)

95568189031753829654…12556160280264888319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.556 × 10⁹⁹(100-digit number)

95568189031753829654…12556160280264888321

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

1.911 × 10¹⁰⁰(101-digit number)

19113637806350765930…25112320560529776639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.911 × 10¹⁰⁰(101-digit number)

19113637806350765930…25112320560529776641

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