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Block #222,986

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/22/2013, 3:43:44 PM Β· Difficulty 9.9390 Β· 6,604,078 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b084a86740b4e3dd5b7a076d42c9f7725f15014c200abf826c77b5e1dc7b7c47
View on Chainz β†—

Height

#222,986

Difficulty

9.939028

Transactions

1

Size

196 B

Version

2

Bits

09f06425

Nonce

234,086

Timestamp

10/22/2013, 3:43:44 PM

Confirmations

6,604,078

Mined by

⛏️ P2SHAc2JS7vmXMnQfMU2dfv3RqLvVFKLzHMXXR

Merkle Root

6862eeb9815d422d2c708fcc8174be5175c48e926f722bfc4fe82a753e66d2ce
Transactions (1)
Coinbase6862eeb9815d42…e82a753e66d2ce
1 in β†’ 1 out10.1100 XPM109 B
Ac2JS7vm…KLzHMXXR
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.

1.319 Γ— 10⁸⁸(89-digit number)
13192662462473608522…55540182726501468399
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
1.319 Γ— 10⁸⁸(89-digit number)
13192662462473608522…55540182726501468399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.638 Γ— 10⁸⁸(89-digit number)
26385324924947217044…11080365453002936799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.277 Γ— 10⁸⁸(89-digit number)
52770649849894434089…22160730906005873599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.055 Γ— 10⁸⁹(90-digit number)
10554129969978886817…44321461812011747199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.110 Γ— 10⁸⁹(90-digit number)
21108259939957773635…88642923624023494399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.221 Γ— 10⁸⁹(90-digit number)
42216519879915547271…77285847248046988799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.443 Γ— 10⁸⁹(90-digit number)
84433039759831094542…54571694496093977599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.688 Γ— 10⁹⁰(91-digit number)
16886607951966218908…09143388992187955199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.377 Γ— 10⁹⁰(91-digit number)
33773215903932437817…18286777984375910399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.754 Γ— 10⁹⁰(91-digit number)
67546431807864875634…36573555968751820799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,860,696 XPMΒ·at block #6,827,063 Β· updates every 60s
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