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Block #2,655,076

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/9/2018, 9:22:30 PM Β· Difficulty 11.7103 Β· 4,190,223 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3a5b32547470f79ffe7b7fe499a0c03935e1e9449222cd67a0b7c8502a8ac010
View on Chainz β†—

Height

#2,655,076

Difficulty

11.710258

Transactions

1

Size

201 B

Version

2

Bits

0bb5d378

Nonce

1,081,442,604

Timestamp

5/9/2018, 9:22:30 PM

Confirmations

4,190,223

Mined by

⛏️ P2SHAQ6emynHFjSaDsBKRe9cu1fB3DBDd7rbGe

Merkle Root

01ab5aed2ebc667c3fc9c2651129a7e43f88de839c9bd9f2b0308e9817a85c8b
Transactions (1)
Coinbase01ab5aed2ebc66…308e9817a85c8b
1 in β†’ 1 out7.2800 XPM110 B
AQ6emynH…BDd7rbGe
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.

9.580 Γ— 10⁹⁢(97-digit number)
95807964345465201192…42257686040905144319
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
9.580 Γ— 10⁹⁢(97-digit number)
95807964345465201192…42257686040905144319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.916 Γ— 10⁹⁷(98-digit number)
19161592869093040238…84515372081810288639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.832 Γ— 10⁹⁷(98-digit number)
38323185738186080476…69030744163620577279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.664 Γ— 10⁹⁷(98-digit number)
76646371476372160953…38061488327241154559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.532 Γ— 10⁹⁸(99-digit number)
15329274295274432190…76122976654482309119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.065 Γ— 10⁹⁸(99-digit number)
30658548590548864381…52245953308964618239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.131 Γ— 10⁹⁸(99-digit number)
61317097181097728763…04491906617929236479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.226 Γ— 10⁹⁹(100-digit number)
12263419436219545752…08983813235858472959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.452 Γ— 10⁹⁹(100-digit number)
24526838872439091505…17967626471716945919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.905 Γ— 10⁹⁹(100-digit number)
49053677744878183010…35935252943433891839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.810 Γ— 10⁹⁹(100-digit number)
98107355489756366020…71870505886867783679
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:58,006,831 XPMΒ·at block #6,845,298 Β· updates every 60s
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