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Block #2,742,217

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/10/2018, 6:44:17 AM Β· Difficulty 11.6313 Β· 4,089,507 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fdedd55cab6a5c3083cb11ca7e6054bfac0c068ca38a7901e57d38f5cf5f19a2
View on Chainz β†—

Height

#2,742,217

Difficulty

11.631280

Transactions

2

Size

1.43 KB

Version

2

Bits

0ba19b95

Nonce

896,325,595

Timestamp

7/10/2018, 6:44:17 AM

Confirmations

4,089,507

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

e168a4ec8f17ca0bbcad3ce2f0ec88d43d94028b0e55cd33b372f8ab74388de0
Transactions (2)
Coinbase4b1eb7b8173172…af4cf412c42419
1 in β†’ 1 out7.4000 XPM109 B
AZtxQr2F…7grUWrUz
ea77abdf5fd164…b5251ea18db75e
8 in β†’ 2 out9986.8300 XPM1.23 KB
AQrqo1fo…CcjbT7toALssV9Qd…PvJB43wd
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.

1.599 Γ— 10⁹⁡(96-digit number)
15996170489366309674…67087650663030778881
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
1.599 Γ— 10⁹⁡(96-digit number)
15996170489366309674…67087650663030778881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.199 Γ— 10⁹⁡(96-digit number)
31992340978732619349…34175301326061557761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.398 Γ— 10⁹⁡(96-digit number)
63984681957465238698…68350602652123115521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.279 Γ— 10⁹⁢(97-digit number)
12796936391493047739…36701205304246231041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.559 Γ— 10⁹⁢(97-digit number)
25593872782986095479…73402410608492462081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.118 Γ— 10⁹⁢(97-digit number)
51187745565972190958…46804821216984924161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.023 Γ— 10⁹⁷(98-digit number)
10237549113194438191…93609642433969848321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.047 Γ— 10⁹⁷(98-digit number)
20475098226388876383…87219284867939696641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.095 Γ— 10⁹⁷(98-digit number)
40950196452777752766…74438569735879393281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.190 Γ— 10⁹⁷(98-digit number)
81900392905555505533…48877139471758786561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.638 Γ— 10⁹⁸(99-digit number)
16380078581111101106…97754278943517573121
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:57,897,897 XPMΒ·at block #6,831,723 Β· updates every 60s
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