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Block #212,199

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/16/2013, 3:45:01 AM Β· Difficulty 9.9184 Β· 6,597,316 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
72961f07cb777ab07046a1fb67966d474c45eb44fb8a8dde726b084876686cf3
View on Chainz β†—

Height

#212,199

Difficulty

9.918357

Transactions

1

Size

198 B

Version

2

Bits

09eb196f

Nonce

243,214

Timestamp

10/16/2013, 3:45:01 AM

Confirmations

6,597,316

Mined by

⛏️ P2SHAXKgkkDGrogBEHJHSetHJnSBPfJyE5mk6Y

Merkle Root

e8ddc2c1bba89f8be31c6fa172534dc16ac2cba3685d42c5a1e57c8232b87d8b
Transactions (1)
Coinbasee8ddc2c1bba89f…e57c8232b87d8b
1 in β†’ 1 out10.1500 XPM109 B
AXKgkkDG…JyE5mk6Y
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.

5.869 Γ— 10⁹²(93-digit number)
58699879705902897839…02135656938477220319
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
5.869 Γ— 10⁹²(93-digit number)
58699879705902897839…02135656938477220319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.173 Γ— 10⁹³(94-digit number)
11739975941180579567…04271313876954440639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.347 Γ— 10⁹³(94-digit number)
23479951882361159135…08542627753908881279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.695 Γ— 10⁹³(94-digit number)
46959903764722318271…17085255507817762559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.391 Γ— 10⁹³(94-digit number)
93919807529444636543…34170511015635525119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.878 Γ— 10⁹⁴(95-digit number)
18783961505888927308…68341022031271050239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.756 Γ— 10⁹⁴(95-digit number)
37567923011777854617…36682044062542100479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.513 Γ— 10⁹⁴(95-digit number)
75135846023555709235…73364088125084200959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.502 Γ— 10⁹⁡(96-digit number)
15027169204711141847…46728176250168401919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,720,196 XPMΒ·at block #6,809,514 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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