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Block #109,876

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/10/2013, 4:24:55 PM Β· Difficulty 9.6816 Β· 6,685,421 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
509f58839f979f0dfce268db25c23eb49d1f21f644c866190841a3a8c6579c5f
View on Chainz β†—

Height

#109,876

Difficulty

9.681559

Transactions

3

Size

878 B

Version

2

Bits

09ae7aa1

Nonce

29,695

Timestamp

8/10/2013, 4:24:55 PM

Confirmations

6,685,421

Mined by

⛏️ P2SHAe1Ai2aZkgQzyZwZt59A2b88wxgwYrcU7U

Merkle Root

cf2bb359830b31d89cb253f0566015f002ebdf8f89301125b4d87cd78552001c
Transactions (3)
Coinbase3a0dd70f27555d…b97e31622efbbd
1 in β†’ 1 out10.6700 XPM109 B
Ae1Ai2aZ…gwYrcU7U
90aed1d27c3fbc…7c1b4a9e6b7165
3 in β†’ 2 out475.0100 XPM523 B
AMu2GgwA…S7qsYR3tANNZSe6V…4n6oJfPa
ed391facf5ff73…9a3e4046cddec4
1 in β†’ 1 out10.8000 XPM157 B
AQj5CF31…Sfv2KzXY
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— 10⁹³(94-digit number)
25335618894148825631…15002725449104573101
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— 10⁹³(94-digit number)
25335618894148825631…15002725449104573101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.067 Γ— 10⁹³(94-digit number)
50671237788297651263…30005450898209146201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.013 Γ— 10⁹⁴(95-digit number)
10134247557659530252…60010901796418292401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.026 Γ— 10⁹⁴(95-digit number)
20268495115319060505…20021803592836584801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.053 Γ— 10⁹⁴(95-digit number)
40536990230638121010…40043607185673169601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.107 Γ— 10⁹⁴(95-digit number)
81073980461276242021…80087214371346339201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.621 Γ— 10⁹⁡(96-digit number)
16214796092255248404…60174428742692678401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.242 Γ— 10⁹⁡(96-digit number)
32429592184510496808…20348857485385356801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.485 Γ— 10⁹⁡(96-digit number)
64859184369020993617…40697714970770713601
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:57,606,428 XPMΒ·at block #6,795,296 Β· updates every 60s
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