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Block #296,292

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/5/2013, 10:39:16 PM Β· Difficulty 9.9917 Β· 6,507,038 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
614a031ca5b5fb5d3bc5b56ffab6dffb9e8b42628020a21b678493971423b23f
View on Chainz β†—

Height

#296,292

Difficulty

9.991651

Transactions

1

Size

1.11 KB

Version

2

Bits

09fddcdc

Nonce

60,444

Timestamp

12/5/2013, 10:39:16 PM

Confirmations

6,507,038

Mined by

⛏️ daRcAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

b5b1211aacd561a88c2fb41290687373ed7264b1805b549cf602eaa3a1424c38
Transactions (1)
Coinbaseb5b1211aacd561…02eaa3a1424c38
1 in β†’ 29 out9.9800 XPM1.02 KB
AQwRN8bE…V8PsTcY9AKEwr54i…9BfmMkRhAYo2ea2S…MM8T4BiQAWuSjViu…6ogxMMq6Aekx7F9R…HJmj5ecv
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.

1.000 Γ— 10⁹⁷(98-digit number)
10001019869104536906…57315837738644570881
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
1.000 Γ— 10⁹⁷(98-digit number)
10001019869104536906…57315837738644570881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.000 Γ— 10⁹⁷(98-digit number)
20002039738209073812…14631675477289141761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.000 Γ— 10⁹⁷(98-digit number)
40004079476418147624…29263350954578283521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.000 Γ— 10⁹⁷(98-digit number)
80008158952836295248…58526701909156567041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.600 Γ— 10⁹⁸(99-digit number)
16001631790567259049…17053403818313134081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.200 Γ— 10⁹⁸(99-digit number)
32003263581134518099…34106807636626268161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.400 Γ— 10⁹⁸(99-digit number)
64006527162269036198…68213615273252536321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.280 Γ— 10⁹⁹(100-digit number)
12801305432453807239…36427230546505072641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.560 Γ— 10⁹⁹(100-digit number)
25602610864907614479…72854461093010145281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.120 Γ— 10⁹⁹(100-digit number)
51205221729815228958…45708922186020290561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
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 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:57,670,671 XPMΒ·at block #6,803,329 Β· updates every 60s
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