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Block #28,424

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 12:15:56 PM Β· Difficulty 7.9819 Β· 6,770,582 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8f9e8aa0c72200dfc72d453cceb4cd2bf88f340d4b8cb1b6603892f6cbdddae1
View on Chainz β†—

Height

#28,424

Difficulty

7.981880

Transactions

1

Size

198 B

Version

2

Bits

07fb5c84

Nonce

1,430

Timestamp

7/13/2013, 12:15:56 PM

Confirmations

6,770,582

Mined by

⛏️ P2SHAV3Mx3AqCBr85EUqewYnyDKYAdAKiwER2W

Merkle Root

d32853ffcca0a2883460478ba51bb7c7c75818e2a98a35db2d0a2d940c448997
Transactions (1)
Coinbased32853ffcca0a2…0a2d940c448997
1 in β†’ 1 out15.6800 XPM109 B
AV3Mx3Aq…AKiwER2W
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.

2.063 Γ— 10⁹³(94-digit number)
20634147491338072351…47333043153176556501
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
2.063 Γ— 10⁹³(94-digit number)
20634147491338072351…47333043153176556501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.126 Γ— 10⁹³(94-digit number)
41268294982676144703…94666086306353113001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.253 Γ— 10⁹³(94-digit number)
82536589965352289407…89332172612706226001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.650 Γ— 10⁹⁴(95-digit number)
16507317993070457881…78664345225412452001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.301 Γ— 10⁹⁴(95-digit number)
33014635986140915763…57328690450824904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.602 Γ— 10⁹⁴(95-digit number)
66029271972281831526…14657380901649808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.320 Γ— 10⁹⁡(96-digit number)
13205854394456366305…29314761803299616001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.641 Γ— 10⁹⁡(96-digit number)
26411708788912732610…58629523606599232001
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:57,636,090 XPMΒ·at block #6,799,005 Β· updates every 60s
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