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Block #263,070

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/17/2013, 11:21:52 AM Β· Difficulty 9.9671 Β· 6,551,024 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
acac9b0677bf6bec51133567faab739eeae35cb5873e5aa2e3d4f33c35cc84e8
View on Chainz β†—

Height

#263,070

Difficulty

9.967105

Transactions

1

Size

187 B

Version

2

Bits

09f7942a

Nonce

272,512

Timestamp

11/17/2013, 11:21:52 AM

Confirmations

6,551,024

Mined by

⛏️ aRALFhmsQiS6Rmx2z4TKGpe8y4dcV5bffJmU

Merkle Root

3cf31bbafa5fee0692ed4855248a789d2607d748931fc25c947fd92103222e29
Transactions (1)
Coinbase3cf31bbafa5fee…7fd92103222e29
1 in β†’ 1 out10.0500 XPM97 B
ALFhmsQi…V5bffJmU
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.

1.507 Γ— 10⁹⁴(95-digit number)
15073239864572467886…56022895370849831521
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
1.507 Γ— 10⁹⁴(95-digit number)
15073239864572467886…56022895370849831521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.014 Γ— 10⁹⁴(95-digit number)
30146479729144935773…12045790741699663041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.029 Γ— 10⁹⁴(95-digit number)
60292959458289871546…24091581483399326081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.205 Γ— 10⁹⁡(96-digit number)
12058591891657974309…48183162966798652161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.411 Γ— 10⁹⁡(96-digit number)
24117183783315948618…96366325933597304321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.823 Γ— 10⁹⁡(96-digit number)
48234367566631897237…92732651867194608641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.646 Γ— 10⁹⁡(96-digit number)
96468735133263794474…85465303734389217281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.929 Γ— 10⁹⁢(97-digit number)
19293747026652758894…70930607468778434561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.858 Γ— 10⁹⁢(97-digit number)
38587494053305517789…41861214937556869121
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
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