Block #2,672,466

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.

8.420 × 10⁹⁶(97-digit number)

84202971930800650281…68665888843120010241

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

8.420 × 10⁹⁶(97-digit number)

84202971930800650281…68665888843120010241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.684 × 10⁹⁷(98-digit number)

16840594386160130056…37331777686240020481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.368 × 10⁹⁷(98-digit number)

33681188772320260112…74663555372480040961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.736 × 10⁹⁷(98-digit number)

67362377544640520225…49327110744960081921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.347 × 10⁹⁸(99-digit number)

13472475508928104045…98654221489920163841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.694 × 10⁹⁸(99-digit number)

26944951017856208090…97308442979840327681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.388 × 10⁹⁸(99-digit number)

53889902035712416180…94616885959680655361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.077 × 10⁹⁹(100-digit number)

10777980407142483236…89233771919361310721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.155 × 10⁹⁹(100-digit number)

21555960814284966472…78467543838722621441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.311 × 10⁹⁹(100-digit number)

43111921628569932944…56935087677445242881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

8.622 × 10⁹⁹(100-digit number)

86223843257139865888…13870175354890485761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

1.724 × 10¹⁰⁰(101-digit number)

17244768651427973177…27740350709780971521

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 #2,672,466

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