Block #1,440,475

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/3/2016, 4:04:54 AM · Difficulty 10.7702 · 5,393,314 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7cceee619ec9c7a60e0e5329d28ea6e36f0cc56ddb2efb2027ec3cc393457186

View on Chainz ↗

Height

#1,440,475

Difficulty

10.770160

Transactions

Size

798 B

Version

Bits

0ac5292d

Nonce

1,793,669,902

Timestamp

2/3/2016, 4:04:54 AM

Confirmations

5,393,314

Mined by

⛏️ P2SHAH6h6gq3mndTpTTmMFZtmF3sPHyi64nX7k

Merkle Root

0ac122eb170bae6186c2cb1a712732223c5a70d7b825461a6e99742dc512963f

Transactions (2)

Coinbasef409ea7042988c…6b2f6ee9ae88e1

1 in → 1 out8.6200 XPM109 B

AH6h6gq3…yi64nX7k

df15c385f7fb88…6edb76cbd9f8b9

1 in → 13 out81.0183 XPM599 B

AMKGtgoh…WjT1Tjsk AVm1tXyB…GSFqxcYX AQyqHKVP…QHymEUvn AQSP1GjG…5GNwyn56 AGyZ5NNX…wMNKccYx

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.

4.271 × 10⁹³(94-digit number)

42712261633854712305…56408811134615858199

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

4.271 × 10⁹³(94-digit number)

42712261633854712305…56408811134615858199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.271 × 10⁹³(94-digit number)

42712261633854712305…56408811134615858201

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

8.542 × 10⁹³(94-digit number)

85424523267709424610…12817622269231716399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.542 × 10⁹³(94-digit number)

85424523267709424610…12817622269231716401

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

1.708 × 10⁹⁴(95-digit number)

17084904653541884922…25635244538463432799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.708 × 10⁹⁴(95-digit number)

17084904653541884922…25635244538463432801

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

3.416 × 10⁹⁴(95-digit number)

34169809307083769844…51270489076926865599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.416 × 10⁹⁴(95-digit number)

34169809307083769844…51270489076926865601

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

6.833 × 10⁹⁴(95-digit number)

68339618614167539688…02540978153853731199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.833 × 10⁹⁴(95-digit number)

68339618614167539688…02540978153853731201

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 #1,440,475

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