Block #2,925,300

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.

1.640 × 10⁹⁴(95-digit number)

16401427473593461657…93898714862457262499

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

1.640 × 10⁹⁴(95-digit number)

16401427473593461657…93898714862457262499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.280 × 10⁹⁴(95-digit number)

32802854947186923315…87797429724914524999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.560 × 10⁹⁴(95-digit number)

65605709894373846631…75594859449829049999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.312 × 10⁹⁵(96-digit number)

13121141978874769326…51189718899658099999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.624 × 10⁹⁵(96-digit number)

26242283957749538652…02379437799316199999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.248 × 10⁹⁵(96-digit number)

52484567915499077305…04758875598632399999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.049 × 10⁹⁶(97-digit number)

10496913583099815461…09517751197264799999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.099 × 10⁹⁶(97-digit number)

20993827166199630922…19035502394529599999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.198 × 10⁹⁶(97-digit number)

41987654332399261844…38071004789059199999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.397 × 10⁹⁶(97-digit number)

83975308664798523688…76142009578118399999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

1.679 × 10⁹⁷(98-digit number)

16795061732959704737…52284019156236799999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^11 × origin − 1

3.359 × 10⁹⁷(98-digit number)

33590123465919409475…04568038312473599999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^12 × origin − 1

6.718 × 10⁹⁷(98-digit number)

67180246931838818950…09136076624947199999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 13 consecutive prime numbers forming a Cunningham Chain of the First 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

LegendaryChain length 13

Roughly 1 in 100,000 blocks. Extremely rare — celebrated by the community.

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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #2,925,300

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