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Block #2,719,801

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/24/2018, 9:05:04 PM Β· Difficulty 11.6126 Β· 4,122,162 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3f26cf4236ebe52b3d0422ef3eec1be0e8232cd7bd312300ed2275f29a9490a2
View on Chainz β†—

Height

#2,719,801

Difficulty

11.612595

Transactions

1

Size

198 B

Version

2

Bits

0b9cd300

Nonce

355,556,320

Timestamp

6/24/2018, 9:05:04 PM

Confirmations

4,122,162

Mined by

⛏️ P2SHAKVZ4Dv7TCdyR188Apt8znBny5MaP8hypg

Merkle Root

b0b36b67a360479112f331cad8db606fb7fda3f5a46da32cf230de1b179b39ff
Transactions (1)
Coinbaseb0b36b67a36047…30de1b179b39ff
1 in β†’ 1 out7.4000 XPM109 B
AKVZ4Dv7…MaP8hypg
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.

7.384 Γ— 10⁹¹(92-digit number)
73847639641589037411…80771990217545613281
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
7.384 Γ— 10⁹¹(92-digit number)
73847639641589037411…80771990217545613281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.476 Γ— 10⁹²(93-digit number)
14769527928317807482…61543980435091226561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.953 Γ— 10⁹²(93-digit number)
29539055856635614964…23087960870182453121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.907 Γ— 10⁹²(93-digit number)
59078111713271229928…46175921740364906241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.181 Γ— 10⁹³(94-digit number)
11815622342654245985…92351843480729812481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.363 Γ— 10⁹³(94-digit number)
23631244685308491971…84703686961459624961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.726 Γ— 10⁹³(94-digit number)
47262489370616983943…69407373922919249921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.452 Γ— 10⁹³(94-digit number)
94524978741233967886…38814747845838499841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.890 Γ— 10⁹⁴(95-digit number)
18904995748246793577…77629495691676999681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.780 Γ— 10⁹⁴(95-digit number)
37809991496493587154…55258991383353999361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.561 Γ— 10⁹⁴(95-digit number)
75619982992987174309…10517982766707998721
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:57,980,086 XPMΒ·at block #6,841,962 Β· updates every 60s
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