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Block #2,469,306

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/12/2018, 10:32:53 AM Β· Difficulty 10.9600 Β· 4,357,770 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d50650f0e5002baaa2a0257f72bc316f84fb0e3980681cbe857db89c8fd954ae
View on Chainz β†—

Height

#2,469,306

Difficulty

10.960022

Transactions

1

Size

199 B

Version

2

Bits

0af5c408

Nonce

472,982,539

Timestamp

1/12/2018, 10:32:53 AM

Confirmations

4,357,770

Mined by

⛏️ P2SHAWGsGxAa5DZq2d9qtr9YEwbfsfeExq1WGY

Merkle Root

ab913a67eb7add7e140fa44a66b831c56987c9070ebb2e0fef51321ce43db676
Transactions (1)
Coinbaseab913a67eb7add…51321ce43db676
1 in β†’ 1 out8.3100 XPM109 B
AWGsGxAa…eExq1WGY
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.

2.846 Γ— 10⁹⁴(95-digit number)
28461813886629716862…54258874714177497601
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
2.846 Γ— 10⁹⁴(95-digit number)
28461813886629716862…54258874714177497601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.692 Γ— 10⁹⁴(95-digit number)
56923627773259433725…08517749428354995201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.138 Γ— 10⁹⁡(96-digit number)
11384725554651886745…17035498856709990401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.276 Γ— 10⁹⁡(96-digit number)
22769451109303773490…34070997713419980801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.553 Γ— 10⁹⁡(96-digit number)
45538902218607546980…68141995426839961601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.107 Γ— 10⁹⁡(96-digit number)
91077804437215093960…36283990853679923201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.821 Γ— 10⁹⁢(97-digit number)
18215560887443018792…72567981707359846401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.643 Γ— 10⁹⁢(97-digit number)
36431121774886037584…45135963414719692801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.286 Γ— 10⁹⁢(97-digit number)
72862243549772075168…90271926829439385601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.457 Γ— 10⁹⁷(98-digit number)
14572448709954415033…80543853658878771201
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:57,860,792 XPMΒ·at block #6,827,075 Β· updates every 60s
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