Block #803,214

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/8/2014, 9:58:52 PM · Difficulty 10.9759 · 6,023,886 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

df7c42bdccdfbcbd4eb7816463df8df0daeb836d7f61ef29af6ef410cd062673

View on Chainz ↗

Height

#803,214

Difficulty

10.975881

Transactions

Size

202 B

Version

Bits

0af9d353

Nonce

104,757

Timestamp

11/8/2014, 9:58:52 PM

Confirmations

6,023,886

Mined by

⛏️ P2SHAJhr6wenio3Wgde7Dyqy4HhXVhDAq9Tpnu

Merkle Root

0dc8e9d7953cc199e69e8fc9793d2ca65807f07bdb754d2b8db9916d392de76e

Transactions (1)

Coinbase0dc8e9d7953cc1…b9916d392de76e

1 in → 1 out8.2900 XPM109 B

AJhr6wen…DAq9Tpnu

Prime Chain Origin

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.

1.572 × 10¹⁰¹(102-digit number)

15721333319755384524…88658846528509651999

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

1.572 × 10¹⁰¹(102-digit number)

15721333319755384524…88658846528509651999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.144 × 10¹⁰¹(102-digit number)

31442666639510769048…77317693057019303999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.288 × 10¹⁰¹(102-digit number)

62885333279021538096…54635386114038607999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.257 × 10¹⁰²(103-digit number)

12577066655804307619…09270772228077215999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.515 × 10¹⁰²(103-digit number)

25154133311608615238…18541544456154431999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.030 × 10¹⁰²(103-digit number)

50308266623217230477…37083088912308863999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.006 × 10¹⁰³(104-digit number)

10061653324643446095…74166177824617727999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.012 × 10¹⁰³(104-digit number)

20123306649286892190…48332355649235455999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.024 × 10¹⁰³(104-digit number)

40246613298573784381…96664711298470911999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.049 × 10¹⁰³(104-digit number)

80493226597147568763…93329422596941823999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #803,214

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