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Block #202,038

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/9/2013, 11:36:53 PM Β· Difficulty 9.8942 Β· 6,601,393 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3d1e6d95753583ca756ff938cbc58bfa2ec380d9fd0aae635d64d32a8c0a53c9
View on Chainz β†—

Height

#202,038

Difficulty

9.894194

Transactions

1

Size

200 B

Version

2

Bits

09e4e9ee

Nonce

24,488

Timestamp

10/9/2013, 11:36:53 PM

Confirmations

6,601,393

Mined by

⛏️ P2SHAZ9gwDSQ9eWoQY9W5dUGn7b9Zwha77qwDk

Merkle Root

44b58617b4bbd902d7654a0f22f04e45e9c8c6acf7b07fb63ab9b9c008c25c6a
Transactions (1)
Coinbase44b58617b4bbd9…b9b9c008c25c6a
1 in β†’ 1 out10.2000 XPM109 B
AZ9gwDSQ…ha77qwDk
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.

4.801 Γ— 10⁹⁢(97-digit number)
48013505191594452580…73705629708017294081
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
4.801 Γ— 10⁹⁢(97-digit number)
48013505191594452580…73705629708017294081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.602 Γ— 10⁹⁢(97-digit number)
96027010383188905161…47411259416034588161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.920 Γ— 10⁹⁷(98-digit number)
19205402076637781032…94822518832069176321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.841 Γ— 10⁹⁷(98-digit number)
38410804153275562064…89645037664138352641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.682 Γ— 10⁹⁷(98-digit number)
76821608306551124129…79290075328276705281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.536 Γ— 10⁹⁸(99-digit number)
15364321661310224825…58580150656553410561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.072 Γ— 10⁹⁸(99-digit number)
30728643322620449651…17160301313106821121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.145 Γ— 10⁹⁸(99-digit number)
61457286645240899303…34320602626213642241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.229 Γ— 10⁹⁹(100-digit number)
12291457329048179860…68641205252427284481
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:57,671,481 XPMΒ·at block #6,803,430 Β· updates every 60s
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