Block #483,635

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2014, 3:58:48 AM · Difficulty 10.5670 · 6,326,291 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5bf75deda4a677295b8229645ceab641d3ea9a180fa60ab3baaa17cfe321e363

View on Chainz ↗

Height

#483,635

Difficulty

10.566956

Transactions

Size

935 B

Version

Bits

0a912400

Nonce

389,344

Timestamp

4/10/2014, 3:58:48 AM

Confirmations

6,326,291

Mined by

⛏️ 3aaSFUtAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e7832a492df96a7a51d09bc3a86de8e6003fb405abe3f318de13e9ba0125757a

Transactions (1)

Coinbasee7832a492df96a…13e9ba0125757a

1 in → 23 out8.9400 XPM845 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 AQ8QAT3J…rCFKuVbR AWMrD5hP…ZwsoxvZ3 ATKK7iFz…wZm46KN1

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.

1.312 × 10⁹⁵(96-digit number)

13127458849516646953…68250428671383820939

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

1.312 × 10⁹⁵(96-digit number)

13127458849516646953…68250428671383820939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.312 × 10⁹⁵(96-digit number)

13127458849516646953…68250428671383820941

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

2.625 × 10⁹⁵(96-digit number)

26254917699033293907…36500857342767641879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.625 × 10⁹⁵(96-digit number)

26254917699033293907…36500857342767641881

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

5.250 × 10⁹⁵(96-digit number)

52509835398066587815…73001714685535283759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.250 × 10⁹⁵(96-digit number)

52509835398066587815…73001714685535283761

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

1.050 × 10⁹⁶(97-digit number)

10501967079613317563…46003429371070567519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.050 × 10⁹⁶(97-digit number)

10501967079613317563…46003429371070567521

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

2.100 × 10⁹⁶(97-digit number)

21003934159226635126…92006858742141135039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.100 × 10⁹⁶(97-digit number)

21003934159226635126…92006858742141135041

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 #483,635

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