Block #369,483

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2014, 10:44:16 AM · Difficulty 10.4448 · 6,457,391 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7534b821d7981e154452c15b3f23e1529ca61e926dd6e3c4ea1174e79082abd

View on Chainz ↗

Height

#369,483

Difficulty

10.444761

Transactions

Size

1.34 KB

Version

Bits

0a71dbd6

Nonce

116,487

Timestamp

1/21/2014, 10:44:16 AM

Confirmations

6,457,391

Mined by

⛏️ KaROAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1bfd80eb4b6e4bb92f2071e9f5abd95e717d070d0c37df3059a5697bdb9d3ecb

Transactions (2)

Coinbase1afb3f96d48a11…19f1ca1590b161

1 in → 25 out9.1500 XPM913 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AZemWJAo…6jhDtieG AYtDvcGs…VuAcA7m7

d507faeaaf2278…9e6e0cbb29d741

2 in → 2 out36.5768 XPM373 B

AYR4TmjH…epDZ4ufW AYNWTamG…bDWTaniT

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.

3.341 × 10⁹⁶(97-digit number)

33410668903850684473…08663096103705111999

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

3.341 × 10⁹⁶(97-digit number)

33410668903850684473…08663096103705111999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.341 × 10⁹⁶(97-digit number)

33410668903850684473…08663096103705112001

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

6.682 × 10⁹⁶(97-digit number)

66821337807701368947…17326192207410223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.682 × 10⁹⁶(97-digit number)

66821337807701368947…17326192207410224001

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

1.336 × 10⁹⁷(98-digit number)

13364267561540273789…34652384414820447999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.336 × 10⁹⁷(98-digit number)

13364267561540273789…34652384414820448001

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

2.672 × 10⁹⁷(98-digit number)

26728535123080547579…69304768829640895999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.672 × 10⁹⁷(98-digit number)

26728535123080547579…69304768829640896001

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

5.345 × 10⁹⁷(98-digit number)

53457070246161095158…38609537659281791999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.345 × 10⁹⁷(98-digit number)

53457070246161095158…38609537659281792001

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 #369,483

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