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Block #918,668

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/1/2015, 2:16:16 PM Β· Difficulty 10.9216 Β· 5,876,094 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eacde3ab19fb527ccf7bb2ca403efccf7fdd8e8cb11dea7eac8d50be354870c5
View on Chainz β†—

Height

#918,668

Difficulty

10.921645

Transactions

2

Size

19.23 KB

Version

2

Bits

0aebf0ee

Nonce

410,276,113

Timestamp

2/1/2015, 2:16:16 PM

Confirmations

5,876,094

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

28f42398a211894fbfc0e85ba38dfc9f0a18c1d26b7d10a95eba8e3159c0ead1
Transactions (2)
Coinbasea755c98f2d794b…44695631dc090b
1 in β†’ 1 out8.5700 XPM116 B
ANSXnLY2…Sd25TjkD
c4423206dd7074…0dfb40601ac522
131 in β†’ 2 out6518.7429 XPM19.02 KB
ASCp5W5b…tECvusW4AcmvPfge…nETo71nD
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.

2.617 Γ— 10⁹⁡(96-digit number)
26172047329330062028…86539826828664273501
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
2.617 Γ— 10⁹⁡(96-digit number)
26172047329330062028…86539826828664273501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.234 Γ— 10⁹⁡(96-digit number)
52344094658660124057…73079653657328547001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.046 Γ— 10⁹⁢(97-digit number)
10468818931732024811…46159307314657094001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.093 Γ— 10⁹⁢(97-digit number)
20937637863464049622…92318614629314188001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.187 Γ— 10⁹⁢(97-digit number)
41875275726928099245…84637229258628376001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.375 Γ— 10⁹⁢(97-digit number)
83750551453856198491…69274458517256752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.675 Γ— 10⁹⁷(98-digit number)
16750110290771239698…38548917034513504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.350 Γ— 10⁹⁷(98-digit number)
33500220581542479396…77097834069027008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.700 Γ— 10⁹⁷(98-digit number)
67000441163084958793…54195668138054016001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.340 Γ— 10⁹⁸(99-digit number)
13400088232616991758…08391336276108032001
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:57,602,144 XPMΒ·at block #6,794,761 Β· updates every 60s
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