Block #549,816

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.

6.343 × 10⁹⁷(98-digit number)

63438513705067743284…47996566675222682059

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

6.343 × 10⁹⁷(98-digit number)

63438513705067743284…47996566675222682059

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.343 × 10⁹⁷(98-digit number)

63438513705067743284…47996566675222682061

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

1.268 × 10⁹⁸(99-digit number)

12687702741013548656…95993133350445364119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.268 × 10⁹⁸(99-digit number)

12687702741013548656…95993133350445364121

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

2.537 × 10⁹⁸(99-digit number)

25375405482027097313…91986266700890728239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.537 × 10⁹⁸(99-digit number)

25375405482027097313…91986266700890728241

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

5.075 × 10⁹⁸(99-digit number)

50750810964054194627…83972533401781456479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.075 × 10⁹⁸(99-digit number)

50750810964054194627…83972533401781456481

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

1.015 × 10⁹⁹(100-digit number)

10150162192810838925…67945066803562912959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.015 × 10⁹⁹(100-digit number)

10150162192810838925…67945066803562912961

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

2.030 × 10⁹⁹(100-digit number)

20300324385621677850…35890133607125825919

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 #549,816

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