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Block #2,654,835

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/9/2018, 4:17:59 PM Β· Difficulty 11.7139 Β· 4,186,944 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cc730b0c86617459966e5212fd2d6aba36dcf78049fb0dafb4ba8979926f7f32
View on Chainz β†—

Height

#2,654,835

Difficulty

11.713871

Transactions

2

Size

427 B

Version

2

Bits

0bb6c045

Nonce

200,278,886

Timestamp

5/9/2018, 4:17:59 PM

Confirmations

4,186,944

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

cdac3cfda61f491fcc208e7f12713b3612a7808f83374f82dd6a72549e45329c
Transactions (2)
Coinbase3acd0eb3d31698…caf79c9fc91a31
1 in β†’ 1 out7.2900 XPM110 B
Adqah8zh…1WwoHJ9t
a44674e6a10807…3f696471927660
1 in β†’ 2 out1.2420 XPM227 B
ARb4rLcS…HNnqv3ofAVx6d7U9…LykyNYqv
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.

1.184 Γ— 10⁹⁡(96-digit number)
11845121242579324100…89103991653107694081
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
1.184 Γ— 10⁹⁡(96-digit number)
11845121242579324100…89103991653107694081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.369 Γ— 10⁹⁡(96-digit number)
23690242485158648200…78207983306215388161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.738 Γ— 10⁹⁡(96-digit number)
47380484970317296400…56415966612430776321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.476 Γ— 10⁹⁡(96-digit number)
94760969940634592800…12831933224861552641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.895 Γ— 10⁹⁢(97-digit number)
18952193988126918560…25663866449723105281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.790 Γ— 10⁹⁢(97-digit number)
37904387976253837120…51327732899446210561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.580 Γ— 10⁹⁢(97-digit number)
75808775952507674240…02655465798892421121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.516 Γ— 10⁹⁷(98-digit number)
15161755190501534848…05310931597784842241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.032 Γ— 10⁹⁷(98-digit number)
30323510381003069696…10621863195569684481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.064 Γ— 10⁹⁷(98-digit number)
60647020762006139392…21243726391139368961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.212 Γ— 10⁹⁸(99-digit number)
12129404152401227878…42487452782278737921
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:57,978,608 XPMΒ·at block #6,841,778 Β· updates every 60s
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