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Block #2,576,117

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/20/2018, 4:06:41 PM Β· Difficulty 10.9956 Β· 4,265,899 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b9b98afaffe48e79b4e5d24a2f5b549b938c1ece65ae18e14086875b49297055
View on Chainz β†—

Height

#2,576,117

Difficulty

10.995648

Transactions

1

Size

200 B

Version

2

Bits

0afee2cb

Nonce

344,684,729

Timestamp

3/20/2018, 4:06:41 PM

Confirmations

4,265,899

Mined by

⛏️ P2SHAWB1QYFybUu8SocwuJ8SGtaDEr6n5CMTf3

Merkle Root

b9c552a9f3c60a6f92a9ee6146c7d175e3b8e8782e9b818c7f75d9e541101a77
Transactions (1)
Coinbaseb9c552a9f3c60a…75d9e541101a77
1 in β†’ 1 out8.2600 XPM110 B
AWB1QYFy…6n5CMTf3
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.

7.753 Γ— 10⁹⁴(95-digit number)
77530102617835959305…84094731855925374399
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
7.753 Γ— 10⁹⁴(95-digit number)
77530102617835959305…84094731855925374399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.550 Γ— 10⁹⁡(96-digit number)
15506020523567191861…68189463711850748799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.101 Γ— 10⁹⁡(96-digit number)
31012041047134383722…36378927423701497599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.202 Γ— 10⁹⁡(96-digit number)
62024082094268767444…72757854847402995199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.240 Γ— 10⁹⁢(97-digit number)
12404816418853753488…45515709694805990399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.480 Γ— 10⁹⁢(97-digit number)
24809632837707506977…91031419389611980799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.961 Γ— 10⁹⁢(97-digit number)
49619265675415013955…82062838779223961599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.923 Γ— 10⁹⁢(97-digit number)
99238531350830027910…64125677558447923199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.984 Γ— 10⁹⁷(98-digit number)
19847706270166005582…28251355116895846399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.969 Γ— 10⁹⁷(98-digit number)
39695412540332011164…56502710233791692799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.939 Γ— 10⁹⁷(98-digit number)
79390825080664022328…13005420467583385599
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,980,515 XPMΒ·at block #6,842,015 Β· updates every 60s
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