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Block #2,856,479

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/27/2018, 1:11:02 AM Β· Difficulty 11.6914 Β· 3,984,833 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
089264df9e0156bb06ea2b685b068aa2463b92b9c3278865d29d482b4394f36f
View on Chainz β†—

Height

#2,856,479

Difficulty

11.691359

Transactions

1

Size

199 B

Version

2

Bits

0bb0fcdf

Nonce

1,316,210,662

Timestamp

9/27/2018, 1:11:02 AM

Confirmations

3,984,833

Mined by

⛏️ P2SHAGWVmszjBPtMVbFwm9xa6HNU4kamB72g5Z

Merkle Root

25d16ef31dfee05555ea9817817aee35072949880bb5ec4873c92acf6df51f38
Transactions (1)
Coinbase25d16ef31dfee0…c92acf6df51f38
1 in β†’ 1 out7.3000 XPM110 B
AGWVmszj…amB72g5Z
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.

8.808 Γ— 10⁹¹(92-digit number)
88086753202285197334…83071403228339288701
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
8.808 Γ— 10⁹¹(92-digit number)
88086753202285197334…83071403228339288701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.761 Γ— 10⁹²(93-digit number)
17617350640457039466…66142806456678577401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.523 Γ— 10⁹²(93-digit number)
35234701280914078933…32285612913357154801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.046 Γ— 10⁹²(93-digit number)
70469402561828157867…64571225826714309601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.409 Γ— 10⁹³(94-digit number)
14093880512365631573…29142451653428619201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.818 Γ— 10⁹³(94-digit number)
28187761024731263146…58284903306857238401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.637 Γ— 10⁹³(94-digit number)
56375522049462526293…16569806613714476801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.127 Γ— 10⁹⁴(95-digit number)
11275104409892505258…33139613227428953601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.255 Γ— 10⁹⁴(95-digit number)
22550208819785010517…66279226454857907201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.510 Γ— 10⁹⁴(95-digit number)
45100417639570021035…32558452909715814401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.020 Γ— 10⁹⁴(95-digit number)
90200835279140042070…65116905819431628801
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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