Block #314,256

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.

2.559 × 10⁹⁸(99-digit number)

25594879033656716060…53119256236916809499

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

2.559 × 10⁹⁸(99-digit number)

25594879033656716060…53119256236916809499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.559 × 10⁹⁸(99-digit number)

25594879033656716060…53119256236916809501

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

5.118 × 10⁹⁸(99-digit number)

51189758067313432121…06238512473833618999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.118 × 10⁹⁸(99-digit number)

51189758067313432121…06238512473833619001

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

1.023 × 10⁹⁹(100-digit number)

10237951613462686424…12477024947667237999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.023 × 10⁹⁹(100-digit number)

10237951613462686424…12477024947667238001

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

2.047 × 10⁹⁹(100-digit number)

20475903226925372848…24954049895334475999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.047 × 10⁹⁹(100-digit number)

20475903226925372848…24954049895334476001

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

4.095 × 10⁹⁹(100-digit number)

40951806453850745697…49908099790668951999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.095 × 10⁹⁹(100-digit number)

40951806453850745697…49908099790668952001

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

8.190 × 10⁹⁹(100-digit number)

81903612907701491395…99816199581337903999

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 #314,256

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