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Block #141,184

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/30/2013, 3:32:12 AM Β· Difficulty 9.8349 Β· 6,654,769 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
62eb8a3d0feb5c62cc404e3652f9818e079ed66edac9b998aff5422b9398ef99
View on Chainz β†—

Height

#141,184

Difficulty

9.834943

Transactions

1

Size

198 B

Version

2

Bits

09d5bed9

Nonce

204,702

Timestamp

8/30/2013, 3:32:12 AM

Confirmations

6,654,769

Mined by

⛏️ P2SHAX99MLNmm1FbkFRt6WY4Zu9rUBvtidqEwE

Merkle Root

44ab087a8b263f57ac135525fada4e8bbd5bd8f16943f912862852ba57f1112a
Transactions (1)
Coinbase44ab087a8b263f…2852ba57f1112a
1 in β†’ 1 out10.3200 XPM109 B
AX99MLNm…vtidqEwE
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.

2.533 Γ— 10⁹²(93-digit number)
25331089258963638711…50467965754492864801
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
2.533 Γ— 10⁹²(93-digit number)
25331089258963638711…50467965754492864801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.066 Γ— 10⁹²(93-digit number)
50662178517927277423…00935931508985729601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.013 Γ— 10⁹³(94-digit number)
10132435703585455484…01871863017971459201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.026 Γ— 10⁹³(94-digit number)
20264871407170910969…03743726035942918401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.052 Γ— 10⁹³(94-digit number)
40529742814341821938…07487452071885836801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.105 Γ— 10⁹³(94-digit number)
81059485628683643877…14974904143771673601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.621 Γ— 10⁹⁴(95-digit number)
16211897125736728775…29949808287543347201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.242 Γ— 10⁹⁴(95-digit number)
32423794251473457551…59899616575086694401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.484 Γ— 10⁹⁴(95-digit number)
64847588502946915102…19799233150173388801
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:57,611,714 XPMΒ·at block #6,795,952 Β· updates every 60s
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