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Block #2,878,322

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/12/2018, 4:56:14 PM Β· Difficulty 11.6462 Β· 3,966,935 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
03594b78a0d396998470b65c2a7706b35b701c2b3fb3ccf84f01752a62b441d8
View on Chainz β†—

Height

#2,878,322

Difficulty

11.646203

Transactions

1

Size

200 B

Version

2

Bits

0ba56d96

Nonce

643,428,985

Timestamp

10/12/2018, 4:56:14 PM

Confirmations

3,966,935

Mined by

⛏️ P2SHAe4kE46ocMY1cSa8ircVj697dd9Lc3BRNN

Merkle Root

64d248bb0b2c263556b8a1c888a40ee4680427e785f270704010718cf9011a79
Transactions (1)
Coinbase64d248bb0b2c26…10718cf9011a79
1 in β†’ 1 out7.3600 XPM110 B
Ae4kE46o…9Lc3BRNN
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.

4.032 Γ— 10⁹⁴(95-digit number)
40324757000870858311…94797117239062597761
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
4.032 Γ— 10⁹⁴(95-digit number)
40324757000870858311…94797117239062597761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.064 Γ— 10⁹⁴(95-digit number)
80649514001741716623…89594234478125195521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.612 Γ— 10⁹⁡(96-digit number)
16129902800348343324…79188468956250391041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.225 Γ— 10⁹⁡(96-digit number)
32259805600696686649…58376937912500782081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.451 Γ— 10⁹⁡(96-digit number)
64519611201393373298…16753875825001564161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.290 Γ— 10⁹⁢(97-digit number)
12903922240278674659…33507751650003128321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.580 Γ— 10⁹⁢(97-digit number)
25807844480557349319…67015503300006256641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.161 Γ— 10⁹⁢(97-digit number)
51615688961114698639…34031006600012513281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.032 Γ— 10⁹⁷(98-digit number)
10323137792222939727…68062013200025026561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.064 Γ— 10⁹⁷(98-digit number)
20646275584445879455…36124026400050053121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.129 Γ— 10⁹⁷(98-digit number)
41292551168891758911…72248052800100106241
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
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