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Block #2,811,500

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2018, 1:25:08 AM Β· Difficulty 11.6672 Β· 4,031,712 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6881a9553ec692f68756fe772ba8ecec66e225c5d73c05a6dfac2aea78a468f8
View on Chainz β†—

Height

#2,811,500

Difficulty

11.667182

Transactions

1

Size

200 B

Version

2

Bits

0baacc77

Nonce

301,589,190

Timestamp

8/27/2018, 1:25:08 AM

Confirmations

4,031,712

Mined by

⛏️ P2SHAL2shDbCrFaNY9UfZFFhBYndUpSdSnomaB

Merkle Root

587f0a512c53bc1c88651489e3a4d4947d5ff55e8ccb258c224c757382556e54
Transactions (1)
Coinbase587f0a512c53bc…4c757382556e54
1 in β†’ 1 out7.3300 XPM110 B
AL2shDbC…SdSnomaB
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.

5.918 Γ— 10⁹³(94-digit number)
59187022599197467216…40704686025668927999
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
5.918 Γ— 10⁹³(94-digit number)
59187022599197467216…40704686025668927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.183 Γ— 10⁹⁴(95-digit number)
11837404519839493443…81409372051337855999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.367 Γ— 10⁹⁴(95-digit number)
23674809039678986886…62818744102675711999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.734 Γ— 10⁹⁴(95-digit number)
47349618079357973773…25637488205351423999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.469 Γ— 10⁹⁴(95-digit number)
94699236158715947546…51274976410702847999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.893 Γ— 10⁹⁡(96-digit number)
18939847231743189509…02549952821405695999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.787 Γ— 10⁹⁡(96-digit number)
37879694463486379018…05099905642811391999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.575 Γ— 10⁹⁡(96-digit number)
75759388926972758037…10199811285622783999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.515 Γ— 10⁹⁢(97-digit number)
15151877785394551607…20399622571245567999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.030 Γ— 10⁹⁢(97-digit number)
30303755570789103214…40799245142491135999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.060 Γ— 10⁹⁢(97-digit number)
60607511141578206429…81598490284982271999
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:57,990,069 XPMΒ·at block #6,843,211 Β· updates every 60s
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