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Block #2,641,359

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 7:55:37 AM Β· Difficulty 11.6176 Β· 4,199,024 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8484e2da9b33d7960f7b538598dc1b8c8c46d012e67006c493e07de6d87d6f75
View on Chainz β†—

Height

#2,641,359

Difficulty

11.617577

Transactions

1

Size

199 B

Version

2

Bits

0b9e1984

Nonce

39,137,930

Timestamp

5/1/2018, 7:55:37 AM

Confirmations

4,199,024

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

9810adb8cc747698cade6aa6a41d992760ea75b6b093d0cf0631405bf2a58fe7
Transactions (1)
Coinbase9810adb8cc7476…31405bf2a58fe7
1 in β†’ 1 out7.4000 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.994 Γ— 10⁹³(94-digit number)
19946002039588789262…13455826111484626251
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
1.994 Γ— 10⁹³(94-digit number)
19946002039588789262…13455826111484626251
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.989 Γ— 10⁹³(94-digit number)
39892004079177578524…26911652222969252501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.978 Γ— 10⁹³(94-digit number)
79784008158355157049…53823304445938505001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.595 Γ— 10⁹⁴(95-digit number)
15956801631671031409…07646608891877010001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.191 Γ— 10⁹⁴(95-digit number)
31913603263342062819…15293217783754020001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.382 Γ— 10⁹⁴(95-digit number)
63827206526684125639…30586435567508040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.276 Γ— 10⁹⁡(96-digit number)
12765441305336825127…61172871135016080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.553 Γ— 10⁹⁡(96-digit number)
25530882610673650255…22345742270032160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.106 Γ— 10⁹⁡(96-digit number)
51061765221347300511…44691484540064320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.021 Γ— 10⁹⁢(97-digit number)
10212353044269460102…89382969080128640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.042 Γ— 10⁹⁢(97-digit number)
20424706088538920204…78765938160257280001
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:57,967,385 XPMΒ·at block #6,840,382 Β· updates every 60s
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