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Block #2,576,509

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/20/2018, 9:15:32 PM Β· Difficulty 10.9957 Β· 4,268,323 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d3136c2013688c48b671c7f82ca6a8df1a34998001c31e7ce9b72d38ca2035c6
View on Chainz β†—

Height

#2,576,509

Difficulty

10.995731

Transactions

1

Size

199 B

Version

2

Bits

0afee83a

Nonce

66,892,012

Timestamp

3/20/2018, 9:15:32 PM

Confirmations

4,268,323

Mined by

⛏️ P2SHAaXySm4ESvdec8iFq5ZMtfbvsxkTodkJf1

Merkle Root

b588e2745ff4dc261d8e67425da7fda5596a600689103817af31a29bb475e53a
Transactions (1)
Coinbaseb588e2745ff4dc…31a29bb475e53a
1 in β†’ 1 out8.2600 XPM109 B
AaXySm4E…kTodkJf1
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.

3.571 Γ— 10⁹⁴(95-digit number)
35712864215330015523…29837933248733109921
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
3.571 Γ— 10⁹⁴(95-digit number)
35712864215330015523…29837933248733109921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.142 Γ— 10⁹⁴(95-digit number)
71425728430660031046…59675866497466219841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.428 Γ— 10⁹⁡(96-digit number)
14285145686132006209…19351732994932439681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.857 Γ— 10⁹⁡(96-digit number)
28570291372264012418…38703465989864879361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.714 Γ— 10⁹⁡(96-digit number)
57140582744528024837…77406931979729758721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.142 Γ— 10⁹⁢(97-digit number)
11428116548905604967…54813863959459517441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.285 Γ— 10⁹⁢(97-digit number)
22856233097811209934…09627727918919034881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.571 Γ— 10⁹⁢(97-digit number)
45712466195622419869…19255455837838069761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.142 Γ— 10⁹⁢(97-digit number)
91424932391244839739…38510911675676139521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.828 Γ— 10⁹⁷(98-digit number)
18284986478248967947…77021823351352279041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.656 Γ— 10⁹⁷(98-digit number)
36569972956497935895…54043646702704558081
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
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