Block #395,218

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2014, 1:31:53 PM · Difficulty 10.4131 · 6,411,562 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b4e2a24f00ba3024a4a904febe914c20dfe779bab723959e64438e721521b6d4

View on Chainz ↗

Height

#395,218

Difficulty

10.413127

Transactions

Size

5.02 KB

Version

Bits

0a69c2af

Nonce

303,692

Timestamp

2/8/2014, 1:31:53 PM

Confirmations

6,411,562

Mined by

⛏️ P2SHAWT4FajAqvKnh9YhmpgjgT5GAa7qUxCsaJ

Merkle Root

fef0a541b6378d85e06062b7074aa76f5729feb250b10a7648f3ec36a929f723

Transactions (4)

Coinbase23b6e7611c5097…c5c6bae59b621a

1 in → 1 out9.2800 XPM109 B

AWT4FajA…7qUxCsaJ

7cd6f70e4c5398…62924c361232ad

27 in → 1 out27.0780 XPM3.95 KB

AYkBGFMC…hunQjHzh

81637ff45cbe15…bd1b656d3b696c

1 in → 2 out2.5232 XPM227 B

AdqH4QjD…3vhGVHG4 AKCS4GWs…xY53bJj1

ad44a4437784ef…ee9e70dc9525c3

4 in → 2 out3.1913 XPM671 B

AdpsxmtJ…ZWfmvRK9 AJ6iqsjd…TsoG6BRU

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.

4.401 × 10¹⁰³(104-digit number)

44013052850524819049…67021269520643960319

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

4.401 × 10¹⁰³(104-digit number)

44013052850524819049…67021269520643960319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.401 × 10¹⁰³(104-digit number)

44013052850524819049…67021269520643960321

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

8.802 × 10¹⁰³(104-digit number)

88026105701049638099…34042539041287920639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.802 × 10¹⁰³(104-digit number)

88026105701049638099…34042539041287920641

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

1.760 × 10¹⁰⁴(105-digit number)

17605221140209927619…68085078082575841279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.760 × 10¹⁰⁴(105-digit number)

17605221140209927619…68085078082575841281

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

3.521 × 10¹⁰⁴(105-digit number)

35210442280419855239…36170156165151682559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.521 × 10¹⁰⁴(105-digit number)

35210442280419855239…36170156165151682561

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

7.042 × 10¹⁰⁴(105-digit number)

70420884560839710479…72340312330303365119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.042 × 10¹⁰⁴(105-digit number)

70420884560839710479…72340312330303365121

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 #395,218

Cookie Preferences