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Block #2,835,380

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2018, 2:23:57 AM Β· Difficulty 11.7158 Β· 4,005,796 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e63360b39d28748cb059c651fd61b4947a4ecdc0fe89d81dd19bb9c841888699
View on Chainz β†—

Height

#2,835,380

Difficulty

11.715815

Transactions

2

Size

6.34 KB

Version

2

Bits

0bb73fa2

Nonce

196,753,972

Timestamp

9/12/2018, 2:23:57 AM

Confirmations

4,005,796

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

b019ef98aa297785d327fd939b1410836d413dbfe434c9247e68e65ee8b1ca6c
Transactions (2)
Coinbase63a9c45e8377de…7217de139bacb5
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
17f5e08493cfe9…2c5935a7a87100
42 in β†’ 2 out19209.6681 XPM6.14 KB
ALwCQx7z…tGh5qLQZAMLggddy…HpikgH98
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.

1.926 Γ— 10⁹³(94-digit number)
19260998667402388599…11654739047047301121
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
1.926 Γ— 10⁹³(94-digit number)
19260998667402388599…11654739047047301121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.852 Γ— 10⁹³(94-digit number)
38521997334804777198…23309478094094602241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.704 Γ— 10⁹³(94-digit number)
77043994669609554396…46618956188189204481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.540 Γ— 10⁹⁴(95-digit number)
15408798933921910879…93237912376378408961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.081 Γ— 10⁹⁴(95-digit number)
30817597867843821758…86475824752756817921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.163 Γ— 10⁹⁴(95-digit number)
61635195735687643517…72951649505513635841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.232 Γ— 10⁹⁡(96-digit number)
12327039147137528703…45903299011027271681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.465 Γ— 10⁹⁡(96-digit number)
24654078294275057406…91806598022054543361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.930 Γ— 10⁹⁡(96-digit number)
49308156588550114813…83613196044109086721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.861 Γ— 10⁹⁡(96-digit number)
98616313177100229627…67226392088218173441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.972 Γ— 10⁹⁢(97-digit number)
19723262635420045925…34452784176436346881
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:57,973,766 XPMΒ·at block #6,841,175 Β· updates every 60s
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