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Block #2,300,062

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/18/2017, 9:30:28 AM Β· Difficulty 10.9348 Β· 4,541,625 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
764626362dc6c9ba7d2eecb9c07a6bc4e4757d553fc644498be6a5ca9c24fceb
View on Chainz β†—

Height

#2,300,062

Difficulty

10.934816

Transactions

1

Size

200 B

Version

2

Bits

0aef5022

Nonce

860,701,383

Timestamp

9/18/2017, 9:30:28 AM

Confirmations

4,541,625

Mined by

⛏️ P2SHAHfGXPm4owx3RhVY3L8AzTDSv1RxZcfV39

Merkle Root

2bf159489d090039b50634a1ad4d4ef63cba7ecd4fdd9dc649461017d52f0a32
Transactions (1)
Coinbase2bf159489d0900…461017d52f0a32
1 in β†’ 1 out8.3500 XPM110 B
AHfGXPm4…RxZcfV39
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.

6.700 Γ— 10⁹⁴(95-digit number)
67000318112906950120…78256764460185933801
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
6.700 Γ— 10⁹⁴(95-digit number)
67000318112906950120…78256764460185933801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.340 Γ— 10⁹⁡(96-digit number)
13400063622581390024…56513528920371867601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.680 Γ— 10⁹⁡(96-digit number)
26800127245162780048…13027057840743735201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.360 Γ— 10⁹⁡(96-digit number)
53600254490325560096…26054115681487470401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.072 Γ— 10⁹⁢(97-digit number)
10720050898065112019…52108231362974940801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.144 Γ— 10⁹⁢(97-digit number)
21440101796130224038…04216462725949881601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.288 Γ— 10⁹⁢(97-digit number)
42880203592260448077…08432925451899763201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.576 Γ— 10⁹⁢(97-digit number)
85760407184520896154…16865850903799526401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.715 Γ— 10⁹⁷(98-digit number)
17152081436904179230…33731701807599052801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.430 Γ— 10⁹⁷(98-digit number)
34304162873808358461…67463403615198105601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.860 Γ— 10⁹⁷(98-digit number)
68608325747616716923…34926807230396211201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,977,884 XPMΒ·at block #6,841,686 Β· updates every 60s
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