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Block #313,104

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/15/2013, 7:49:35 AM Β· Difficulty 9.9960 Β· 6,514,053 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cee52b5b9dd6afc9e483834bbbfedf85b5d2837b641d4bcef49b34b62b9e5325
View on Chainz β†—

Height

#313,104

Difficulty

9.996023

Transactions

1

Size

198 B

Version

2

Bits

09fefb57

Nonce

7,434

Timestamp

12/15/2013, 7:49:35 AM

Confirmations

6,514,053

Mined by

⛏️ P2SHAM1A9CZLPnH51axL7hPRTWjkm6as4Lpogj

Merkle Root

9825e66b403ac7bf9c7c915776151602be3f82f0c3d3c047855a0239eb80ad3f
Transactions (1)
Coinbase9825e66b403ac7…5a0239eb80ad3f
1 in β†’ 1 out9.9900 XPM109 B
AM1A9CZL…as4Lpogj
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.

1.631 Γ— 10⁹³(94-digit number)
16319919019134340557…81245781185782748001
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
1.631 Γ— 10⁹³(94-digit number)
16319919019134340557…81245781185782748001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.263 Γ— 10⁹³(94-digit number)
32639838038268681114…62491562371565496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.527 Γ— 10⁹³(94-digit number)
65279676076537362228…24983124743130992001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.305 Γ— 10⁹⁴(95-digit number)
13055935215307472445…49966249486261984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.611 Γ— 10⁹⁴(95-digit number)
26111870430614944891…99932498972523968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.222 Γ— 10⁹⁴(95-digit number)
52223740861229889782…99864997945047936001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.044 Γ— 10⁹⁡(96-digit number)
10444748172245977956…99729995890095872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.088 Γ— 10⁹⁡(96-digit number)
20889496344491955912…99459991780191744001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.177 Γ— 10⁹⁡(96-digit number)
41778992688983911825…98919983560383488001
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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