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Block #144,108

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/1/2013, 2:48:00 AM Β· Difficulty 9.8379 Β· 6,682,004 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4a031b9c8f7728f0b6f53a3eeca90feb1530ecce2d1ed036dd97e788d1c5712c
View on Chainz β†—

Height

#144,108

Difficulty

9.837882

Transactions

1

Size

198 B

Version

2

Bits

09d67f6d

Nonce

77,730

Timestamp

9/1/2013, 2:48:00 AM

Confirmations

6,682,004

Mined by

⛏️ P2SHAVJaZtXCr3NXSK79aMri9GXJU2gGZDZ3Yk

Merkle Root

875cdce6a5f2f672de59db8cca12fc2ca4051c940c923b4406e4991f0856f6c0
Transactions (1)
Coinbase875cdce6a5f2f6…e4991f0856f6c0
1 in β†’ 1 out10.3200 XPM109 B
AVJaZtXC…gGZDZ3Yk
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.

1.141 Γ— 10⁹²(93-digit number)
11415847413852770175…98132597928629955281
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
1.141 Γ— 10⁹²(93-digit number)
11415847413852770175…98132597928629955281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.283 Γ— 10⁹²(93-digit number)
22831694827705540350…96265195857259910561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.566 Γ— 10⁹²(93-digit number)
45663389655411080700…92530391714519821121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.132 Γ— 10⁹²(93-digit number)
91326779310822161401…85060783429039642241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.826 Γ— 10⁹³(94-digit number)
18265355862164432280…70121566858079284481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.653 Γ— 10⁹³(94-digit number)
36530711724328864560…40243133716158568961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.306 Γ— 10⁹³(94-digit number)
73061423448657729121…80486267432317137921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.461 Γ— 10⁹⁴(95-digit number)
14612284689731545824…60972534864634275841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.922 Γ— 10⁹⁴(95-digit number)
29224569379463091648…21945069729268551681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.844 Γ— 10⁹⁴(95-digit number)
58449138758926183296…43890139458537103361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,853,020 XPMΒ·at block #6,826,111 Β· updates every 60s
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