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Block #2,637,275

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 9:17:15 PM Β· Difficulty 11.4305 Β· 4,189,799 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3497c5c5e0d132e2485484f98cc7eef64f2f2e089eb833b0a35f46d019499d29
View on Chainz β†—

Height

#2,637,275

Difficulty

11.430519

Transactions

2

Size

719 B

Version

2

Bits

0b6e3676

Nonce

139,973,631

Timestamp

4/29/2018, 9:17:15 PM

Confirmations

4,189,799

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

85d6bce9839ae113d3fd365b50a214df994058e197699d4c17ce397cdd8ca220
Transactions (2)
Coinbase80b7914d141414…d44acb2284af11
1 in β†’ 1 out7.6500 XPM110 B
Adqah8zh…1WwoHJ9t
a3e511b29f8bf1…9c117aeabbde48
3 in β†’ 2 out15.2611 XPM520 B
ALCyLDdk…9jK3XeGpALMJpw1B…SJrXi7pa
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.

2.175 Γ— 10⁹³(94-digit number)
21758236804292142470…85196119921646718801
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
2.175 Γ— 10⁹³(94-digit number)
21758236804292142470…85196119921646718801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.351 Γ— 10⁹³(94-digit number)
43516473608584284940…70392239843293437601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.703 Γ— 10⁹³(94-digit number)
87032947217168569880…40784479686586875201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.740 Γ— 10⁹⁴(95-digit number)
17406589443433713976…81568959373173750401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.481 Γ— 10⁹⁴(95-digit number)
34813178886867427952…63137918746347500801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.962 Γ— 10⁹⁴(95-digit number)
69626357773734855904…26275837492695001601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.392 Γ— 10⁹⁡(96-digit number)
13925271554746971180…52551674985390003201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.785 Γ— 10⁹⁡(96-digit number)
27850543109493942361…05103349970780006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.570 Γ— 10⁹⁡(96-digit number)
55701086218987884723…10206699941560012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.114 Γ— 10⁹⁢(97-digit number)
11140217243797576944…20413399883120025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.228 Γ— 10⁹⁢(97-digit number)
22280434487595153889…40826799766240051201
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:57,860,775 XPMΒ·at block #6,827,073 Β· updates every 60s
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