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Block #125,728

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2013, 10:50:46 AM Β· Difficulty 9.7773 Β· 6,675,015 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
465dded4cd0b30e666112624d54bbf8566860481fb3f229ddead3597cbf88bdc
View on Chainz β†—

Height

#125,728

Difficulty

9.777315

Transactions

1

Size

206 B

Version

2

Bits

09c6fe25

Nonce

1,396,852

Timestamp

8/20/2013, 10:50:46 AM

Confirmations

6,675,015

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

ce73a65a344749f642e83f1167ba1026beae38ef815c11d105f36991293dc255
Transactions (1)
Coinbasece73a65a344749…f36991293dc255
1 in β†’ 1 out10.4500 XPM112 B
AT5A2KL6…CT16n6i2
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.

2.864 Γ— 10¹⁰³(104-digit number)
28641046307850055911…03077335980711884001
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
2.864 Γ— 10¹⁰³(104-digit number)
28641046307850055911…03077335980711884001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.728 Γ— 10¹⁰³(104-digit number)
57282092615700111822…06154671961423768001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.145 Γ— 10¹⁰⁴(105-digit number)
11456418523140022364…12309343922847536001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.291 Γ— 10¹⁰⁴(105-digit number)
22912837046280044729…24618687845695072001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.582 Γ— 10¹⁰⁴(105-digit number)
45825674092560089458…49237375691390144001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.165 Γ— 10¹⁰⁴(105-digit number)
91651348185120178916…98474751382780288001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.833 Γ— 10¹⁰⁡(106-digit number)
18330269637024035783…96949502765560576001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.666 Γ— 10¹⁰⁡(106-digit number)
36660539274048071566…93899005531121152001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.332 Γ— 10¹⁰⁡(106-digit number)
73321078548096143133…87798011062242304001
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:57,650,016 XPMΒ·at block #6,800,742 Β· updates every 60s
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