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Block #441,405

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/13/2014, 2:57:03 AM Β· Difficulty 10.3501 Β· 6,367,350 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5595f79f2f7d9e71cc37f030a0b82f47cb9a8fe4e484d14b9d039be7a38dd788
View on Chainz β†—

Height

#441,405

Difficulty

10.350063

Transactions

2

Size

2.87 KB

Version

2

Bits

0a599db3

Nonce

485,099

Timestamp

3/13/2014, 2:57:03 AM

Confirmations

6,367,350

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

93ff8dae087faf1927c43c088f4097571e5a30924df1033af6f09ad156e6bf07
Transactions (2)
Coinbase843d4759571b32…440b7afda3bf00
1 in β†’ 1 out9.3500 XPM110 B
AeKNrjNj…1NEq95Ta
fff4f67fb80f12…69ab2b74857419
18 in β†’ 2 out8.7193 XPM2.68 KB
AbxwcQ9p…D7vj6xJ5AHF5b1D1…S2iVyevY
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.

2.313 Γ— 10⁹⁸(99-digit number)
23138468493286218653…64987152986103533621
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
2.313 Γ— 10⁹⁸(99-digit number)
23138468493286218653…64987152986103533621
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.627 Γ— 10⁹⁸(99-digit number)
46276936986572437306…29974305972207067241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.255 Γ— 10⁹⁸(99-digit number)
92553873973144874613…59948611944414134481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.851 Γ— 10⁹⁹(100-digit number)
18510774794628974922…19897223888828268961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.702 Γ— 10⁹⁹(100-digit number)
37021549589257949845…39794447777656537921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.404 Γ— 10⁹⁹(100-digit number)
74043099178515899690…79588895555313075841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.480 Γ— 10¹⁰⁰(101-digit number)
14808619835703179938…59177791110626151681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.961 Γ— 10¹⁰⁰(101-digit number)
29617239671406359876…18355582221252303361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.923 Γ— 10¹⁰⁰(101-digit number)
59234479342812719752…36711164442504606721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.184 Γ— 10¹⁰¹(102-digit number)
11846895868562543950…73422328885009213441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,714,088 XPMΒ·at block #6,808,754 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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