Block #3,003,690

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.

1.539 × 10⁹⁴(95-digit number)

15392016434882624548…95814076378048550001

Discovered Prime Numbers

p_k = 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.

origin + 1

1.539 × 10⁹⁴(95-digit number)

15392016434882624548…95814076378048550001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.078 × 10⁹⁴(95-digit number)

30784032869765249097…91628152756097100001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.156 × 10⁹⁴(95-digit number)

61568065739530498194…83256305512194200001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.231 × 10⁹⁵(96-digit number)

12313613147906099638…66512611024388400001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.462 × 10⁹⁵(96-digit number)

24627226295812199277…33025222048776800001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.925 × 10⁹⁵(96-digit number)

49254452591624398555…66050444097553600001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.850 × 10⁹⁵(96-digit number)

98508905183248797110…32100888195107200001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.970 × 10⁹⁶(97-digit number)

19701781036649759422…64201776390214400001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.940 × 10⁹⁶(97-digit number)

39403562073299518844…28403552780428800001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.880 × 10⁹⁶(97-digit number)

78807124146599037688…56807105560857600001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.576 × 10⁹⁷(98-digit number)

15761424829319807537…13614211121715200001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

3.152 × 10⁹⁷(98-digit number)

31522849658639615075…27228422243430400001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the Second Kind. 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #3,003,690

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