Block #46,949

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/15/2013, 8:35:16 AM · Difficulty 8.8075 · 6,743,990 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

02a38fe9002b0379190bbef04d9cd8bd607e24c2553c89f0ecd276468a708bc3

View on Chainz ↗

Height

#46,949

Difficulty

8.807529

Transactions

Size

200 B

Version

Bits

08ceba39

Nonce

107

Timestamp

7/15/2013, 8:35:16 AM

Confirmations

6,743,990

Merkle Root

71aac1434c3aae3f957dbb3a5258df42f4615a757c683c9dfdba03368bf44435

Transactions (1)

Coinbase71aac1434c3aae…ba03368bf44435

1 in → 1 out12.8700 XPM109 B

AFpoZRQr…UDiMcjrB

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.

2.904 × 10⁹⁶(97-digit number)

29048481708559177844…87014086383072001001

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

2.904 × 10⁹⁶(97-digit number)

29048481708559177844…87014086383072001001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.809 × 10⁹⁶(97-digit number)

58096963417118355688…74028172766144002001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.161 × 10⁹⁷(98-digit number)

11619392683423671137…48056345532288004001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.323 × 10⁹⁷(98-digit number)

23238785366847342275…96112691064576008001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.647 × 10⁹⁷(98-digit number)

46477570733694684550…92225382129152016001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.295 × 10⁹⁷(98-digit number)

92955141467389369101…84450764258304032001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.859 × 10⁹⁸(99-digit number)

18591028293477873820…68901528516608064001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.718 × 10⁹⁸(99-digit number)

37182056586955747640…37803057033216128001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.436 × 10⁹⁸(99-digit number)

74364113173911495281…75606114066432256001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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