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Block #203,213

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/10/2013, 5:25:29 PM Β· Difficulty 9.8966 Β· 6,613,184 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a15677267de297d29a7cea7ba42233a340c99f4ea24c0fdae1944cdbf8528dbe
View on Chainz β†—

Height

#203,213

Difficulty

9.896551

Transactions

1

Size

197 B

Version

2

Bits

09e58459

Nonce

208,059

Timestamp

10/10/2013, 5:25:29 PM

Confirmations

6,613,184

Mined by

⛏️ P2SHAP52EE3FezHothJTJo3Xw2Hi1LZhqfNP3e

Merkle Root

2b403ae7e27599c9d63a1207f2720966ad227925a053843e94223fdbf78dfdcb
Transactions (1)
Coinbase2b403ae7e27599…223fdbf78dfdcb
1 in β†’ 1 out10.1900 XPM109 B
AP52EE3F…ZhqfNP3e
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.

3.426 Γ— 10⁸⁹(90-digit number)
34260760662671396978…63638110417528053799
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
3.426 Γ— 10⁸⁹(90-digit number)
34260760662671396978…63638110417528053799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.852 Γ— 10⁸⁹(90-digit number)
68521521325342793957…27276220835056107599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.370 Γ— 10⁹⁰(91-digit number)
13704304265068558791…54552441670112215199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.740 Γ— 10⁹⁰(91-digit number)
27408608530137117583…09104883340224430399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.481 Γ— 10⁹⁰(91-digit number)
54817217060274235166…18209766680448860799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.096 Γ— 10⁹¹(92-digit number)
10963443412054847033…36419533360897721599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.192 Γ— 10⁹¹(92-digit number)
21926886824109694066…72839066721795443199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.385 Γ— 10⁹¹(92-digit number)
43853773648219388132…45678133443590886399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.770 Γ— 10⁹¹(92-digit number)
87707547296438776265…91356266887181772799
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
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