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Block #1,144,194

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/8/2015, 2:50:26 AM Β· Difficulty 10.9279 Β· 5,650,173 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
749ad336e5a5b9eb42a83187f862c808ad0c47ce610b0dfe29a2d518a2eb5266
View on Chainz β†—

Height

#1,144,194

Difficulty

10.927889

Transactions

1

Size

199 B

Version

2

Bits

0aed8a22

Nonce

1,611,846,122

Timestamp

7/8/2015, 2:50:26 AM

Confirmations

5,650,173

Mined by

⛏️ P2SHAVyFLFbihab7xW449DAGe8Pg91EWnXwQ4H

Merkle Root

cda8c85dfaaf1631b9a3acd1b1335e66460911934bea5e7fd2e2b08e157c066d
Transactions (1)
Coinbasecda8c85dfaaf16…e2b08e157c066d
1 in β†’ 1 out8.3600 XPM109 B
AVyFLFbi…EWnXwQ4H
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.

2.713 Γ— 10⁹⁴(95-digit number)
27132882651347252731…73001656797117862401
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
2.713 Γ— 10⁹⁴(95-digit number)
27132882651347252731…73001656797117862401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.426 Γ— 10⁹⁴(95-digit number)
54265765302694505462…46003313594235724801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.085 Γ— 10⁹⁡(96-digit number)
10853153060538901092…92006627188471449601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.170 Γ— 10⁹⁡(96-digit number)
21706306121077802184…84013254376942899201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.341 Γ— 10⁹⁡(96-digit number)
43412612242155604369…68026508753885798401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.682 Γ— 10⁹⁡(96-digit number)
86825224484311208739…36053017507771596801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.736 Γ— 10⁹⁢(97-digit number)
17365044896862241747…72106035015543193601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.473 Γ— 10⁹⁢(97-digit number)
34730089793724483495…44212070031086387201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.946 Γ— 10⁹⁢(97-digit number)
69460179587448966991…88424140062172774401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.389 Γ— 10⁹⁷(98-digit number)
13892035917489793398…76848280124345548801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,598,970 XPMΒ·at block #6,794,366 Β· updates every 60s
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