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Block #159,540

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/11/2013, 4:56:56 AM Β· Difficulty 9.8651 Β· 6,657,157 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9b69ae715bff6cd13940fd7fa7bd3861d805d868c193be6aa78476550e7aa154
View on Chainz β†—

Height

#159,540

Difficulty

9.865136

Transactions

2

Size

356 B

Version

2

Bits

09dd798b

Nonce

124,532

Timestamp

9/11/2013, 4:56:56 AM

Confirmations

6,657,157

Mined by

⛏️ P2SHASiN1vnGnb4VLXNU9Yym429CfsnPBYx4TC

Merkle Root

63ffcb6c03dddcf49f5cf5eaeb29e0dc6dafa14afc4fcd09d3131492346be985
Transactions (2)
Coinbase046cdcfc1137dd…2603133a09f3bd
1 in β†’ 1 out10.2700 XPM109 B
ASiN1vnG…nPBYx4TC
ef804a8d1730f5…9a67f08563b495
1 in β†’ 1 out10.2600 XPM157 B
AMm2NR1w…19uBFzE6
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.

1.955 Γ— 10⁹⁡(96-digit number)
19553579738483531841…42547519583128620801
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
1.955 Γ— 10⁹⁡(96-digit number)
19553579738483531841…42547519583128620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.910 Γ— 10⁹⁡(96-digit number)
39107159476967063683…85095039166257241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.821 Γ— 10⁹⁡(96-digit number)
78214318953934127367…70190078332514483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.564 Γ— 10⁹⁢(97-digit number)
15642863790786825473…40380156665028966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.128 Γ— 10⁹⁢(97-digit number)
31285727581573650946…80760313330057932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.257 Γ— 10⁹⁢(97-digit number)
62571455163147301893…61520626660115865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.251 Γ— 10⁹⁷(98-digit number)
12514291032629460378…23041253320231731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.502 Γ— 10⁹⁷(98-digit number)
25028582065258920757…46082506640463462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.005 Γ— 10⁹⁷(98-digit number)
50057164130517841515…92165013280926924801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,777,698 XPMΒ·at block #6,816,696 Β· updates every 60s
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