Block #391,134

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.

1.019 × 10¹⁰³(104-digit number)

10190338440109252119…36693742702989148159

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

1.019 × 10¹⁰³(104-digit number)

10190338440109252119…36693742702989148159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.019 × 10¹⁰³(104-digit number)

10190338440109252119…36693742702989148161

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

2.038 × 10¹⁰³(104-digit number)

20380676880218504238…73387485405978296319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.038 × 10¹⁰³(104-digit number)

20380676880218504238…73387485405978296321

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

4.076 × 10¹⁰³(104-digit number)

40761353760437008476…46774970811956592639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.076 × 10¹⁰³(104-digit number)

40761353760437008476…46774970811956592641

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

8.152 × 10¹⁰³(104-digit number)

81522707520874016952…93549941623913185279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.152 × 10¹⁰³(104-digit number)

81522707520874016952…93549941623913185281

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

1.630 × 10¹⁰⁴(105-digit number)

16304541504174803390…87099883247826370559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.630 × 10¹⁰⁴(105-digit number)

16304541504174803390…87099883247826370561

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

3.260 × 10¹⁰⁴(105-digit number)

32609083008349606781…74199766495652741119

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 #391,134

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