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Block #30,366

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 6:49:53 PM Β· Difficulty 7.9867 Β· 6,787,445 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c7ea07d1dce275382f795d8414a2c9f76c2b06fe2342cda1223066ef815e487d
View on Chainz β†—

Height

#30,366

Difficulty

7.986721

Transactions

1

Size

197 B

Version

2

Bits

07fc99c7

Nonce

49

Timestamp

7/13/2013, 6:49:53 PM

Confirmations

6,787,445

Mined by

⛏️ P2SHAYTtnr7Z6BXv8TVgkRtfQiVWVSAUx4dVQg

Merkle Root

fff23faac7c580650fa0cb81d3b5706571676b8a34fb382762db082603a9a965
Transactions (1)
Coinbasefff23faac7c580…db082603a9a965
1 in β†’ 1 out15.6600 XPM108 B
AYTtnr7Z…AUx4dVQg
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.

2.020 Γ— 10⁹²(93-digit number)
20209174643234134428…92117330996328002241
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
2.020 Γ— 10⁹²(93-digit number)
20209174643234134428…92117330996328002241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.041 Γ— 10⁹²(93-digit number)
40418349286468268857…84234661992656004481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.083 Γ— 10⁹²(93-digit number)
80836698572936537715…68469323985312008961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.616 Γ— 10⁹³(94-digit number)
16167339714587307543…36938647970624017921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.233 Γ— 10⁹³(94-digit number)
32334679429174615086…73877295941248035841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.466 Γ— 10⁹³(94-digit number)
64669358858349230172…47754591882496071681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.293 Γ— 10⁹⁴(95-digit number)
12933871771669846034…95509183764992143361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,786,549 XPMΒ·at block #6,817,810 Β· updates every 60s
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