Block #827,309

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.

3.043 × 10⁹⁵(96-digit number)

30438833998366649101…71914900671566359359

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

3.043 × 10⁹⁵(96-digit number)

30438833998366649101…71914900671566359359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.043 × 10⁹⁵(96-digit number)

30438833998366649101…71914900671566359361

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

6.087 × 10⁹⁵(96-digit number)

60877667996733298202…43829801343132718719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.087 × 10⁹⁵(96-digit number)

60877667996733298202…43829801343132718721

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

1.217 × 10⁹⁶(97-digit number)

12175533599346659640…87659602686265437439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.217 × 10⁹⁶(97-digit number)

12175533599346659640…87659602686265437441

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

2.435 × 10⁹⁶(97-digit number)

24351067198693319280…75319205372530874879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.435 × 10⁹⁶(97-digit number)

24351067198693319280…75319205372530874881

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

4.870 × 10⁹⁶(97-digit number)

48702134397386638561…50638410745061749759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.870 × 10⁹⁶(97-digit number)

48702134397386638561…50638410745061749761

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

9.740 × 10⁹⁶(97-digit number)

97404268794773277123…01276821490123499519

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 #827,309

Cookie Preferences