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Block #2,576,552

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/20/2018, 9:49:46 PM Β· Difficulty 10.9957 Β· 4,265,628 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4ae7603f5b064e6f249c6d5f6de4e79cb8b23c83cdc29bfac08074d636c4cdf9
View on Chainz β†—

Height

#2,576,552

Difficulty

10.995740

Transactions

1

Size

199 B

Version

2

Bits

0afee8d4

Nonce

392,851,801

Timestamp

3/20/2018, 9:49:46 PM

Confirmations

4,265,628

Mined by

⛏️ P2SHAFwwj5Fi1qYUDSEnQ64xpofMrmMVNHGUvL

Merkle Root

16956fad7e0e9c6dadc3beb91a3a33ce069fb591b63a22bfb97b0019f0c9eb2e
Transactions (1)
Coinbase16956fad7e0e9c…7b0019f0c9eb2e
1 in β†’ 1 out8.2600 XPM109 B
AFwwj5Fi…MVNHGUvL
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.

6.049 Γ— 10⁹⁴(95-digit number)
60491223243194351403…45727358667191334001
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
6.049 Γ— 10⁹⁴(95-digit number)
60491223243194351403…45727358667191334001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.209 Γ— 10⁹⁡(96-digit number)
12098244648638870280…91454717334382668001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.419 Γ— 10⁹⁡(96-digit number)
24196489297277740561…82909434668765336001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.839 Γ— 10⁹⁡(96-digit number)
48392978594555481122…65818869337530672001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.678 Γ— 10⁹⁡(96-digit number)
96785957189110962245…31637738675061344001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.935 Γ— 10⁹⁢(97-digit number)
19357191437822192449…63275477350122688001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.871 Γ— 10⁹⁢(97-digit number)
38714382875644384898…26550954700245376001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.742 Γ— 10⁹⁢(97-digit number)
77428765751288769796…53101909400490752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.548 Γ— 10⁹⁷(98-digit number)
15485753150257753959…06203818800981504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.097 Γ— 10⁹⁷(98-digit number)
30971506300515507918…12407637601963008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.194 Γ— 10⁹⁷(98-digit number)
61943012601031015836…24815275203926016001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,981,832 XPMΒ·at block #6,842,179 Β· updates every 60s
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