Block #1,436,228

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/30/2016, 3:05:34 PM · Difficulty 10.8057 · 5,390,908 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a6460b1aba7374820e6ec729f0997e2f7ee177acc65ade13e0c5b85e1c5828a

View on Chainz ↗

Height

#1,436,228

Difficulty

10.805695

Transactions

Size

1.11 KB

Version

Bits

0ace4203

Nonce

105,060,252

Timestamp

1/30/2016, 3:05:34 PM

Confirmations

5,390,908

Mined by

⛏️ P2SHAKtfhPMk8emG7fR3gKnzRZZg9M7gGcNLF1

Merkle Root

dccea2cda390922b135fc103ee353f8d7b258ced66bf8560e8c0f1597cda1f15

Transactions (2)

Coinbase3dcfc222e6c25b…aa91c8d2b84b32

1 in → 1 out8.5600 XPM110 B

AKtfhPMk…7gGcNLF1

2e79459fd6129c…d23c6083d7607b

1 in → 23 out142.4103 XPM941 B

Ae3mvu1y…WJjV3Hsc AVQBdEzC…8RQ1a7dG AXBiQnT9…8RFMibK2 APPJYbcJ…ytyoL2AK AZHRhjg9…scMau2cC

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.

4.085 × 10⁹⁴(95-digit number)

40855730830148533214…69878923589094138239

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

4.085 × 10⁹⁴(95-digit number)

40855730830148533214…69878923589094138239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.085 × 10⁹⁴(95-digit number)

40855730830148533214…69878923589094138241

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

8.171 × 10⁹⁴(95-digit number)

81711461660297066428…39757847178188276479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.171 × 10⁹⁴(95-digit number)

81711461660297066428…39757847178188276481

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

1.634 × 10⁹⁵(96-digit number)

16342292332059413285…79515694356376552959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.634 × 10⁹⁵(96-digit number)

16342292332059413285…79515694356376552961

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

3.268 × 10⁹⁵(96-digit number)

32684584664118826571…59031388712753105919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.268 × 10⁹⁵(96-digit number)

32684584664118826571…59031388712753105921

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

6.536 × 10⁹⁵(96-digit number)

65369169328237653143…18062777425506211839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.536 × 10⁹⁵(96-digit number)

65369169328237653143…18062777425506211841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.307 × 10⁹⁶(97-digit number)

13073833865647530628…36125554851012423679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,436,228

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