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Block #185,972

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/29/2013, 3:30:11 PM Β· Difficulty 9.8638 Β· 6,617,446 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ace24a3d32bdc0ebb122dd6931848558d3b4a830ae995c4b78d2668003123d76
View on Chainz β†—

Height

#185,972

Difficulty

9.863787

Transactions

1

Size

199 B

Version

2

Bits

09dd2126

Nonce

141,049

Timestamp

9/29/2013, 3:30:11 PM

Confirmations

6,617,446

Mined by

⛏️ P2SHAf4wD75XA9FH57PpXqZqsYip2hLxgjq8Ud

Merkle Root

c64fc24a0b693feb1aa8cadf3d1e256467b30d730d6aea5e5fb387918d2c734d
Transactions (1)
Coinbasec64fc24a0b693f…b387918d2c734d
1 in β†’ 1 out10.2600 XPM109 B
Af4wD75X…Lxgjq8Ud
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.

2.504 Γ— 10⁹⁴(95-digit number)
25048700087744575386…16258679154280908801
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
2.504 Γ— 10⁹⁴(95-digit number)
25048700087744575386…16258679154280908801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.009 Γ— 10⁹⁴(95-digit number)
50097400175489150773…32517358308561817601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.001 Γ— 10⁹⁡(96-digit number)
10019480035097830154…65034716617123635201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.003 Γ— 10⁹⁡(96-digit number)
20038960070195660309…30069433234247270401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.007 Γ— 10⁹⁡(96-digit number)
40077920140391320618…60138866468494540801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.015 Γ— 10⁹⁡(96-digit number)
80155840280782641237…20277732936989081601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.603 Γ— 10⁹⁢(97-digit number)
16031168056156528247…40555465873978163201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.206 Γ— 10⁹⁢(97-digit number)
32062336112313056495…81110931747956326401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.412 Γ— 10⁹⁢(97-digit number)
64124672224626112990…62221863495912652801
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:57,671,375 XPMΒ·at block #6,803,417 Β· updates every 60s
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