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Block #2,717,620

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/23/2018, 7:41:17 AM Β· Difficulty 11.6173 Β· 4,120,409 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9ce917758d65b9a2ffd35841391684b1a673a612f78fdc7a70e3b7cc5ea9de20
View on Chainz β†—

Height

#2,717,620

Difficulty

11.617305

Transactions

1

Size

200 B

Version

2

Bits

0b9e07b1

Nonce

940,889,579

Timestamp

6/23/2018, 7:41:17 AM

Confirmations

4,120,409

Mined by

⛏️ P2SHAZobYqfZBvNSt3MnDBVPZEfuo8etBPMCxp

Merkle Root

3b9dd3dd96656890bbf3c9438672f5c54f647e6bbf6d85319b5013afe6a8d4fc
Transactions (1)
Coinbase3b9dd3dd966568…5013afe6a8d4fc
1 in β†’ 1 out7.4000 XPM109 B
AZobYqfZ…etBPMCxp
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.

2.453 Γ— 10⁹⁢(97-digit number)
24531722094701619678…20258961959266649601
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
2.453 Γ— 10⁹⁢(97-digit number)
24531722094701619678…20258961959266649601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.906 Γ— 10⁹⁢(97-digit number)
49063444189403239357…40517923918533299201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.812 Γ— 10⁹⁢(97-digit number)
98126888378806478714…81035847837066598401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.962 Γ— 10⁹⁷(98-digit number)
19625377675761295742…62071695674133196801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.925 Γ— 10⁹⁷(98-digit number)
39250755351522591485…24143391348266393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.850 Γ— 10⁹⁷(98-digit number)
78501510703045182971…48286782696532787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.570 Γ— 10⁹⁸(99-digit number)
15700302140609036594…96573565393065574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.140 Γ— 10⁹⁸(99-digit number)
31400604281218073188…93147130786131148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.280 Γ— 10⁹⁸(99-digit number)
62801208562436146377…86294261572262297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.256 Γ— 10⁹⁹(100-digit number)
12560241712487229275…72588523144524595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.512 Γ— 10⁹⁹(100-digit number)
25120483424974458550…45177046289049190401
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:57,948,586 XPMΒ·at block #6,838,028 Β· updates every 60s
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