Block #62,392

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 6:56:57 PM · Difficulty 8.9762 · 6,744,228 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
76a83ce2770f40202a41e026196e1de053e5098bde9e32d0281d11c4e1265440

Height

#62,392

Difficulty

8.976247

Transactions

2

Size

1016 B

Version

2

Bits

08f9eb51

Nonce

223

Timestamp

7/18/2013, 6:56:57 PM

Confirmations

6,744,228

Merkle Root

632ea2a6b50b26121980accdd00d60064744025c2b2e107c53f1aae7af6efee3
Transactions (2)
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.

1.995 × 10⁹⁶(97-digit number)
19956923298712944275…20332815676034125911
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.

1
origin + 1
1.995 × 10⁹⁶(97-digit number)
19956923298712944275…20332815676034125911
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.991 × 10⁹⁶(97-digit number)
39913846597425888551…40665631352068251821
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.982 × 10⁹⁶(97-digit number)
79827693194851777103…81331262704136503641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.596 × 10⁹⁷(98-digit number)
15965538638970355420…62662525408273007281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.193 × 10⁹⁷(98-digit number)
31931077277940710841…25325050816546014561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.386 × 10⁹⁷(98-digit number)
63862154555881421682…50650101633092029121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.277 × 10⁹⁸(99-digit number)
12772430911176284336…01300203266184058241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.554 × 10⁹⁸(99-digit number)
25544861822352568673…02600406532368116481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.108 × 10⁹⁸(99-digit number)
51089723644705137346…05200813064736232961
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, …
Circulating Supply:57,697,060 XPM·at block #6,806,619 · updates every 60s
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