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Block #2,822,911

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/3/2018, 1:59:46 PM Β· Difficulty 11.7035 Β· 4,016,994 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9d869422e06fbe3e4f0b74d0b0db05071c13ba6e1161d16b7aedb739491b479f
View on Chainz β†—

Height

#2,822,911

Difficulty

11.703537

Transactions

1

Size

201 B

Version

2

Bits

0bb41afe

Nonce

1,507,579,398

Timestamp

9/3/2018, 1:59:46 PM

Confirmations

4,016,994

Mined by

⛏️ P2SHAWtQmKTMETfbE9WLebvYwU1jcqn3NDNaPm

Merkle Root

0aba5ebd299fa99b2deddb7dc916a853b6664759b9c9adac825ee5dec9883def
Transactions (1)
Coinbase0aba5ebd299fa9…5ee5dec9883def
1 in β†’ 1 out7.2900 XPM110 B
AWtQmKTM…n3NDNaPm
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.

4.726 Γ— 10⁹⁷(98-digit number)
47266973598548686692…73066760657233387521
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
4.726 Γ— 10⁹⁷(98-digit number)
47266973598548686692…73066760657233387521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.453 Γ— 10⁹⁷(98-digit number)
94533947197097373385…46133521314466775041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.890 Γ— 10⁹⁸(99-digit number)
18906789439419474677…92267042628933550081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.781 Γ— 10⁹⁸(99-digit number)
37813578878838949354…84534085257867100161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.562 Γ— 10⁹⁸(99-digit number)
75627157757677898708…69068170515734200321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.512 Γ— 10⁹⁹(100-digit number)
15125431551535579741…38136341031468400641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.025 Γ— 10⁹⁹(100-digit number)
30250863103071159483…76272682062936801281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.050 Γ— 10⁹⁹(100-digit number)
60501726206142318966…52545364125873602561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.210 Γ— 10¹⁰⁰(101-digit number)
12100345241228463793…05090728251747205121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.420 Γ— 10¹⁰⁰(101-digit number)
24200690482456927586…10181456503494410241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.840 Γ— 10¹⁰⁰(101-digit number)
48401380964913855173…20362913006988820481
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:57,963,539 XPMΒ·at block #6,839,904 Β· updates every 60s
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