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Block #41,004

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/14/2013, 3:54:27 PM Β· Difficulty 8.4864 Β· 6,770,100 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c784a41fad2e26196bc9999ac9eabf95beb5f7db1374197e679c2027d5cb15c4
View on Chainz β†—

Height

#41,004

Difficulty

8.486378

Transactions

2

Size

932 B

Version

2

Bits

087c8342

Nonce

358

Timestamp

7/14/2013, 3:54:27 PM

Confirmations

6,770,100

Mined by

⛏️ P2SHAWcGTy4Yh4EG3pfC4uhXcGK9vEMgweDnNi

Merkle Root

86f390eb847ba33e11bb4805628938f225bdca787b87ab3ffd1ca330b182cef5
Transactions (2)
Coinbase831324e6e62118…8b69a66b639010
1 in β†’ 1 out13.8800 XPM110 B
AWcGTy4Y…MgweDnNi
8f8aa0010c9992…181e79931adcb2
6 in β†’ 1 out93.8600 XPM731 B
AWZPS4WA…7LQazeJT
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.

1.060 Γ— 10⁹⁸(99-digit number)
10603033096818536416…89073278747857302431
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
1.060 Γ— 10⁹⁸(99-digit number)
10603033096818536416…89073278747857302431
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.120 Γ— 10⁹⁸(99-digit number)
21206066193637072833…78146557495714604861
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.241 Γ— 10⁹⁸(99-digit number)
42412132387274145667…56293114991429209721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.482 Γ— 10⁹⁸(99-digit number)
84824264774548291335…12586229982858419441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.696 Γ— 10⁹⁹(100-digit number)
16964852954909658267…25172459965716838881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.392 Γ— 10⁹⁹(100-digit number)
33929705909819316534…50344919931433677761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.785 Γ— 10⁹⁹(100-digit number)
67859411819638633068…00689839862867355521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.357 Γ— 10¹⁰⁰(101-digit number)
13571882363927726613…01379679725734711041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,732,939 XPMΒ·at block #6,811,103 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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