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Block #63,318

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2013, 12:42:34 AM Β· Difficulty 8.9789 Β· 6,763,330 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2bd54f0b257fd8eeb69e7797ffef6e34b0b74b0bfa1d74a2740c2260ee107e35
View on Chainz β†—

Height

#63,318

Difficulty

8.978858

Transactions

1

Size

199 B

Version

2

Bits

08fa966b

Nonce

130

Timestamp

7/19/2013, 12:42:34 AM

Confirmations

6,763,330

Mined by

⛏️ P2SHAH3bk8ohLSMBJsQQBkFEekzeoE33SrZ2yc

Merkle Root

457e29e9075c6f66484b6059a62d8e530d2671ad63d33dd90921510264014755
Transactions (1)
Coinbase457e29e9075c6f…21510264014755
1 in β†’ 1 out12.3900 XPM110 B
AH3bk8oh…33SrZ2yc
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.063 Γ— 10⁹³(94-digit number)
10636614769935060361…00487949434795818491
Discovered Prime Numbers
p_k = 2^k Γ— 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
1.063 Γ— 10⁹³(94-digit number)
10636614769935060361…00487949434795818491
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.127 Γ— 10⁹³(94-digit number)
21273229539870120723…00975898869591636981
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.254 Γ— 10⁹³(94-digit number)
42546459079740241447…01951797739183273961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.509 Γ— 10⁹³(94-digit number)
85092918159480482894…03903595478366547921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.701 Γ— 10⁹⁴(95-digit number)
17018583631896096578…07807190956733095841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.403 Γ— 10⁹⁴(95-digit number)
34037167263792193157…15614381913466191681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.807 Γ— 10⁹⁴(95-digit number)
68074334527584386315…31228763826932383361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.361 Γ— 10⁹⁡(96-digit number)
13614866905516877263…62457527653864766721
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 8

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,857,332 XPMΒ·at block #6,826,647 Β· updates every 60s
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