Block #856,034

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.

6.548 × 10⁹⁴(95-digit number)

65486656684715681995…57494665969062170439

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

6.548 × 10⁹⁴(95-digit number)

65486656684715681995…57494665969062170439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.548 × 10⁹⁴(95-digit number)

65486656684715681995…57494665969062170441

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

1.309 × 10⁹⁵(96-digit number)

13097331336943136399…14989331938124340879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.309 × 10⁹⁵(96-digit number)

13097331336943136399…14989331938124340881

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

2.619 × 10⁹⁵(96-digit number)

26194662673886272798…29978663876248681759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.619 × 10⁹⁵(96-digit number)

26194662673886272798…29978663876248681761

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

5.238 × 10⁹⁵(96-digit number)

52389325347772545596…59957327752497363519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.238 × 10⁹⁵(96-digit number)

52389325347772545596…59957327752497363521

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

1.047 × 10⁹⁶(97-digit number)

10477865069554509119…19914655504994727039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.047 × 10⁹⁶(97-digit number)

10477865069554509119…19914655504994727041

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

2.095 × 10⁹⁶(97-digit number)

20955730139109018238…39829311009989454079

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

2.095 × 10⁹⁶(97-digit number)

20955730139109018238…39829311009989454081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #856,034

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