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Block #2,650,364

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2018, 11:57:07 PM Β· Difficulty 11.7571 Β· 4,192,735 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0820498cd957b7bfc809aa98ce8d120238052a9f6fe8afc69d81077ba242ae43
View on Chainz β†—

Height

#2,650,364

Difficulty

11.757142

Transactions

1

Size

200 B

Version

2

Bits

0bc1d40a

Nonce

488,576,546

Timestamp

5/5/2018, 11:57:07 PM

Confirmations

4,192,735

Mined by

⛏️ P2SHAdoY6oUETXh1ti8LFLCWpMVVLgGmD7gsUK

Merkle Root

2d2dc80a0fc7312623c89e8eb689e5acf4475004424ca46fbd378e6ca4b77d16
Transactions (1)
Coinbase2d2dc80a0fc731…378e6ca4b77d16
1 in β†’ 1 out7.2200 XPM110 B
AdoY6oUE…GmD7gsUK
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.

2.173 Γ— 10⁹⁴(95-digit number)
21735205797111311043…63701416002787742701
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
2.173 Γ— 10⁹⁴(95-digit number)
21735205797111311043…63701416002787742701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.347 Γ— 10⁹⁴(95-digit number)
43470411594222622087…27402832005575485401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.694 Γ— 10⁹⁴(95-digit number)
86940823188445244175…54805664011150970801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.738 Γ— 10⁹⁡(96-digit number)
17388164637689048835…09611328022301941601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.477 Γ— 10⁹⁡(96-digit number)
34776329275378097670…19222656044603883201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.955 Γ— 10⁹⁡(96-digit number)
69552658550756195340…38445312089207766401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.391 Γ— 10⁹⁢(97-digit number)
13910531710151239068…76890624178415532801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.782 Γ— 10⁹⁢(97-digit number)
27821063420302478136…53781248356831065601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.564 Γ— 10⁹⁢(97-digit number)
55642126840604956272…07562496713662131201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.112 Γ— 10⁹⁷(98-digit number)
11128425368120991254…15124993427324262401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.225 Γ— 10⁹⁷(98-digit number)
22256850736241982508…30249986854648524801
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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