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Block #2,716,310

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/22/2018, 10:30:24 AM Β· Difficulty 11.6143 Β· 4,121,400 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e8eed5717be18561e0fac0732aa06e08862c225428b8927dc8bced4e33b3e3e8
View on Chainz β†—

Height

#2,716,310

Difficulty

11.614292

Transactions

1

Size

199 B

Version

2

Bits

0b9d423a

Nonce

1,285,678,794

Timestamp

6/22/2018, 10:30:24 AM

Confirmations

4,121,400

Mined by

⛏️ P2SHAeev6dJuhc2KFa5h5emKRz7Z4NPXZw9VLa

Merkle Root

92b12b4828378ecc4567c69e758bdb3000c3742f0f0c56b6e01a77df01fecc29
Transactions (1)
Coinbase92b12b4828378e…1a77df01fecc29
1 in β†’ 1 out7.4000 XPM109 B
Aeev6dJu…PXZw9VLa
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.

1.124 Γ— 10⁹⁴(95-digit number)
11245009005273908714…04837789935001480141
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
1.124 Γ— 10⁹⁴(95-digit number)
11245009005273908714…04837789935001480141
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.249 Γ— 10⁹⁴(95-digit number)
22490018010547817428…09675579870002960281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.498 Γ— 10⁹⁴(95-digit number)
44980036021095634857…19351159740005920561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.996 Γ— 10⁹⁴(95-digit number)
89960072042191269714…38702319480011841121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.799 Γ— 10⁹⁡(96-digit number)
17992014408438253942…77404638960023682241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.598 Γ— 10⁹⁡(96-digit number)
35984028816876507885…54809277920047364481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.196 Γ— 10⁹⁡(96-digit number)
71968057633753015771…09618555840094728961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.439 Γ— 10⁹⁢(97-digit number)
14393611526750603154…19237111680189457921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.878 Γ— 10⁹⁢(97-digit number)
28787223053501206308…38474223360378915841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.757 Γ— 10⁹⁢(97-digit number)
57574446107002412617…76948446720757831681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.151 Γ— 10⁹⁷(98-digit number)
11514889221400482523…53896893441515663361
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:57,946,007 XPMΒ·at block #6,837,709 Β· updates every 60s
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