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Block #875,884

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/30/2014, 10:54:19 PM Β· Difficulty 10.9652 Β· 5,950,873 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1d2c7159d11ead3614ab35b811e306f8cb2060a6b15fbee4001c9b05eef91d44
View on Chainz β†—

Height

#875,884

Difficulty

10.965173

Transactions

1

Size

198 B

Version

2

Bits

0af71592

Nonce

199,073

Timestamp

12/30/2014, 10:54:19 PM

Confirmations

5,950,873

Mined by

⛏️ P2SHAYDZhi2ATcpB6cf15iGzieKf1815tJmJHB

Merkle Root

4539283ca7e4d7e1e220b2e62907d96c4e1cb6e7f616f5e120e77548b8c218dd
Transactions (1)
Coinbase4539283ca7e4d7…e77548b8c218dd
1 in β†’ 1 out8.3000 XPM109 B
AYDZhi2A…15tJmJHB
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.

2.724 Γ— 10⁹³(94-digit number)
27243530942893433340…03846320471811072001
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
2.724 Γ— 10⁹³(94-digit number)
27243530942893433340…03846320471811072001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.448 Γ— 10⁹³(94-digit number)
54487061885786866681…07692640943622144001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.089 Γ— 10⁹⁴(95-digit number)
10897412377157373336…15385281887244288001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.179 Γ— 10⁹⁴(95-digit number)
21794824754314746672…30770563774488576001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.358 Γ— 10⁹⁴(95-digit number)
43589649508629493345…61541127548977152001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.717 Γ— 10⁹⁴(95-digit number)
87179299017258986690…23082255097954304001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.743 Γ— 10⁹⁡(96-digit number)
17435859803451797338…46164510195908608001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.487 Γ— 10⁹⁡(96-digit number)
34871719606903594676…92329020391817216001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.974 Γ— 10⁹⁡(96-digit number)
69743439213807189352…84658040783634432001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.394 Γ— 10⁹⁢(97-digit number)
13948687842761437870…69316081567268864001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.789 Γ— 10⁹⁢(97-digit number)
27897375685522875741…38632163134537728001
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:57,858,214 XPMΒ·at block #6,826,756 Β· updates every 60s
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