Block #86,424

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 3:14:23 AM · Difficulty 9.2889 · 6,705,930 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fec67dbd6dd1e99f0773f0b32222bbf145f2c758684bfe7fda23cbe856a3216f

View on Chainz ↗

Height

#86,424

Difficulty

9.288897

Transactions

Size

205 B

Version

Bits

0949f528

Nonce

110,146

Timestamp

7/28/2013, 3:14:23 AM

Confirmations

6,705,930

Merkle Root

ae6d2bfb136cd8d32157183e1e65b3f985e4fd497b36ec7d864f4a36b9d3e974

Transactions (1)

Coinbaseae6d2bfb136cd8…4f4a36b9d3e974

1 in → 1 out11.5700 XPM109 B

AVkQsqkc…NnZ8vi1V

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.

1.525 × 10¹⁰⁹(110-digit number)

15253877407752174813…80483014985817269899

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

1.525 × 10¹⁰⁹(110-digit number)

15253877407752174813…80483014985817269899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.525 × 10¹⁰⁹(110-digit number)

15253877407752174813…80483014985817269901

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

3.050 × 10¹⁰⁹(110-digit number)

30507754815504349626…60966029971634539799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.050 × 10¹⁰⁹(110-digit number)

30507754815504349626…60966029971634539801

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

6.101 × 10¹⁰⁹(110-digit number)

61015509631008699253…21932059943269079599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.101 × 10¹⁰⁹(110-digit number)

61015509631008699253…21932059943269079601

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

1.220 × 10¹¹⁰(111-digit number)

12203101926201739850…43864119886538159199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.220 × 10¹¹⁰(111-digit number)

12203101926201739850…43864119886538159201

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

2.440 × 10¹¹⁰(111-digit number)

24406203852403479701…87728239773076318399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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