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Block #141,705

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/30/2013, 12:02:14 PM Β· Difficulty 9.8353 Β· 6,674,430 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a9c158007f43765e3bcf2e376d80dbe407d47e483b95269ba50382e67caedce1
View on Chainz β†—

Height

#141,705

Difficulty

9.835337

Transactions

1

Size

199 B

Version

2

Bits

09d5d89d

Nonce

285,674

Timestamp

8/30/2013, 12:02:14 PM

Confirmations

6,674,430

Mined by

⛏️ P2SHAPhf7UNhFmiWTjaLJn2VQXWWmeGDFABLcg

Merkle Root

229d1ec0a9791f2ec9d5b4cd8cbe44e1aa7e56b07c236166eb85329449a8b2fe
Transactions (1)
Coinbase229d1ec0a9791f…85329449a8b2fe
1 in β†’ 1 out10.3200 XPM109 B
APhf7UNh…GDFABLcg
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.

2.164 Γ— 10⁹⁡(96-digit number)
21646289292758690896…79427112964996619601
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.164 Γ— 10⁹⁡(96-digit number)
21646289292758690896…79427112964996619601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.329 Γ— 10⁹⁡(96-digit number)
43292578585517381792…58854225929993239201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.658 Γ— 10⁹⁡(96-digit number)
86585157171034763585…17708451859986478401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.731 Γ— 10⁹⁢(97-digit number)
17317031434206952717…35416903719972956801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.463 Γ— 10⁹⁢(97-digit number)
34634062868413905434…70833807439945913601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.926 Γ— 10⁹⁢(97-digit number)
69268125736827810868…41667614879891827201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.385 Γ— 10⁹⁷(98-digit number)
13853625147365562173…83335229759783654401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.770 Γ— 10⁹⁷(98-digit number)
27707250294731124347…66670459519567308801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.541 Γ— 10⁹⁷(98-digit number)
55414500589462248694…33340919039134617601
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,773,206 XPMΒ·at block #6,816,134 Β· updates every 60s
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