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Block #242,204

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/3/2013, 3:18:27 PM Β· Difficulty 9.9593 Β· 6,574,103 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
82e03f47df4e67696591c457aba1dc63e2744d2877b9d0c4f5c971cce5cb657e
View on Chainz β†—

Height

#242,204

Difficulty

9.959295

Transactions

1

Size

200 B

Version

2

Bits

09f59456

Nonce

1,110

Timestamp

11/3/2013, 3:18:27 PM

Confirmations

6,574,103

Mined by

⛏️ P2SHAWKimBPMQT8AEeEuQZ96qGCDXD2EpmG96V

Merkle Root

aec8e3bc91e794b98398dedeb2015f4ce3c5e36c4f432960e24fd831575659dd
Transactions (1)
Coinbaseaec8e3bc91e794…4fd831575659dd
1 in β†’ 1 out10.0700 XPM109 B
AWKimBPM…2EpmG96V
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.

9.342 Γ— 10⁹⁷(98-digit number)
93420510302402794020…51793591386065994241
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
9.342 Γ— 10⁹⁷(98-digit number)
93420510302402794020…51793591386065994241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.868 Γ— 10⁹⁸(99-digit number)
18684102060480558804…03587182772131988481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.736 Γ— 10⁹⁸(99-digit number)
37368204120961117608…07174365544263976961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.473 Γ— 10⁹⁸(99-digit number)
74736408241922235216…14348731088527953921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.494 Γ— 10⁹⁹(100-digit number)
14947281648384447043…28697462177055907841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.989 Γ— 10⁹⁹(100-digit number)
29894563296768894086…57394924354111815681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.978 Γ— 10⁹⁹(100-digit number)
59789126593537788173…14789848708223631361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.195 Γ— 10¹⁰⁰(101-digit number)
11957825318707557634…29579697416447262721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.391 Γ— 10¹⁰⁰(101-digit number)
23915650637415115269…59159394832894525441
Verify on FactorDB β†—Wolfram Alpha β†—

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 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 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 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
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