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Block #2,821,515

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/2/2018, 2:54:05 PM Β· Difficulty 11.7029 Β· 4,023,196 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a96c51f96836d99b34df45b071daf2ccde72648f134b591859842a68170b8e77
View on Chainz β†—

Height

#2,821,515

Difficulty

11.702892

Transactions

1

Size

200 B

Version

2

Bits

0bb3f0b8

Nonce

580,736,554

Timestamp

9/2/2018, 2:54:05 PM

Confirmations

4,023,196

Mined by

⛏️ P2SHAN6q9gQnbtHZCjNesF8sM1vCj6DAPJzArs

Merkle Root

4400939193b90e34ccd4b6d036d8c0de711646ac1c2facdd62073b4da160fe9d
Transactions (1)
Coinbase4400939193b90e…073b4da160fe9d
1 in β†’ 1 out7.2900 XPM110 B
AN6q9gQn…DAPJzArs
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.

7.531 Γ— 10⁹³(94-digit number)
75310485067333795757…66239351904803733761
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
7.531 Γ— 10⁹³(94-digit number)
75310485067333795757…66239351904803733761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.506 Γ— 10⁹⁴(95-digit number)
15062097013466759151…32478703809607467521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.012 Γ— 10⁹⁴(95-digit number)
30124194026933518302…64957407619214935041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.024 Γ— 10⁹⁴(95-digit number)
60248388053867036605…29914815238429870081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.204 Γ— 10⁹⁡(96-digit number)
12049677610773407321…59829630476859740161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.409 Γ— 10⁹⁡(96-digit number)
24099355221546814642…19659260953719480321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.819 Γ— 10⁹⁡(96-digit number)
48198710443093629284…39318521907438960641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.639 Γ— 10⁹⁡(96-digit number)
96397420886187258569…78637043814877921281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.927 Γ— 10⁹⁢(97-digit number)
19279484177237451713…57274087629755842561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.855 Γ— 10⁹⁢(97-digit number)
38558968354474903427…14548175259511685121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.711 Γ— 10⁹⁢(97-digit number)
77117936708949806855…29096350519023370241
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:58,002,098 XPMΒ·at block #6,844,710 Β· updates every 60s
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