Block #401,556

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/12/2014, 8:32:18 PM · Difficulty 10.4335 · 6,415,870 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

21c40e024ea6e2344da7a1456867bfcc70a9501b1927509fb9440a5db812d8a7

View on Chainz ↗

Height

#401,556

Difficulty

10.433525

Transactions

Size

14.55 KB

Version

Bits

0a6efb7e

Nonce

264,390

Timestamp

2/12/2014, 8:32:18 PM

Confirmations

6,415,870

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

82eb614022f713df7c5c49588017e65bef007d185f1f0b377831dd26f3368aa0

Transactions (3)

Coinbased717f14e1090aa…10273324f48056

1 in → 1 out9.3300 XPM110 B

AeKNrjNj…1NEq95Ta

39f12383dbb141…622db97e7aacea

3 in → 4 out9.3032 XPM557 B

AeKNrjNj…1NEq95Ta AQ85HiFh…1Tu9fuBM AaJDdc7U…2or4KU41 AUdoR1CL…hGjJfPiM

eb8450c01e96bc…486bceff597941

95 in → 2 out450.0103 XPM13.81 KB

AcR41BAn…CBHbdS6o AXpHj8VG…p14M3hZe

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.

1.085 × 10¹⁰¹(102-digit number)

10858456435470119196…42613343206270248959

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

1.085 × 10¹⁰¹(102-digit number)

10858456435470119196…42613343206270248959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.085 × 10¹⁰¹(102-digit number)

10858456435470119196…42613343206270248961

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

2.171 × 10¹⁰¹(102-digit number)

21716912870940238393…85226686412540497919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.171 × 10¹⁰¹(102-digit number)

21716912870940238393…85226686412540497921

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

4.343 × 10¹⁰¹(102-digit number)

43433825741880476787…70453372825080995839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.343 × 10¹⁰¹(102-digit number)

43433825741880476787…70453372825080995841

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

8.686 × 10¹⁰¹(102-digit number)

86867651483760953575…40906745650161991679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.686 × 10¹⁰¹(102-digit number)

86867651483760953575…40906745650161991681

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

1.737 × 10¹⁰²(103-digit number)

17373530296752190715…81813491300323983359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.737 × 10¹⁰²(103-digit number)

17373530296752190715…81813491300323983361

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 #401,556

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