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Block #2,818,335

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/31/2018, 11:17:19 AM Β· Difficulty 11.6978 Β· 4,023,035 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aaaa92ed7166149f8e14317bc37405b1882dff94e0598af40537f27ec6871f22
View on Chainz β†—

Height

#2,818,335

Difficulty

11.697834

Transactions

1

Size

201 B

Version

2

Bits

0bb2a53e

Nonce

1,322,292,098

Timestamp

8/31/2018, 11:17:19 AM

Confirmations

4,023,035

Mined by

⛏️ P2SHAMmFFw3tWbqctrQvu3A544T9pnfsT2KdwE

Merkle Root

0fbd76a406fd9af88cef7af599758aa8e947005af248b957485f59a6c67144c4
Transactions (1)
Coinbase0fbd76a406fd9a…5f59a6c67144c4
1 in β†’ 1 out7.3000 XPM110 B
AMmFFw3t…fsT2KdwE
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.

2.346 Γ— 10⁹⁢(97-digit number)
23467338232846671666…32599169113946193921
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
2.346 Γ— 10⁹⁢(97-digit number)
23467338232846671666…32599169113946193921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.693 Γ— 10⁹⁢(97-digit number)
46934676465693343333…65198338227892387841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.386 Γ— 10⁹⁢(97-digit number)
93869352931386686667…30396676455784775681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.877 Γ— 10⁹⁷(98-digit number)
18773870586277337333…60793352911569551361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.754 Γ— 10⁹⁷(98-digit number)
37547741172554674666…21586705823139102721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.509 Γ— 10⁹⁷(98-digit number)
75095482345109349333…43173411646278205441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.501 Γ— 10⁹⁸(99-digit number)
15019096469021869866…86346823292556410881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.003 Γ— 10⁹⁸(99-digit number)
30038192938043739733…72693646585112821761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.007 Γ— 10⁹⁸(99-digit number)
60076385876087479467…45387293170225643521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.201 Γ— 10⁹⁹(100-digit number)
12015277175217495893…90774586340451287041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.403 Γ— 10⁹⁹(100-digit number)
24030554350434991786…81549172680902574081
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:57,975,330 XPMΒ·at block #6,841,369 Β· updates every 60s
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