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Block #1,099,977

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/11/2015, 1:36:57 PM Β· Difficulty 10.7598 Β· 5,707,643 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b876b8d7c363823fbdfa92be0369cca60e5b8332a6dfb51505e1fc98ae6d527f
View on Chainz β†—

Height

#1,099,977

Difficulty

10.759750

Transactions

1

Size

200 B

Version

2

Bits

0ac27f01

Nonce

45,020,642

Timestamp

6/11/2015, 1:36:57 PM

Confirmations

5,707,643

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

ca42e5e961c0aa4fd6458930fd150f77f884c3a65e749ac2fe9a912db9566b4f
Transactions (1)
Coinbaseca42e5e961c0aa…9a912db9566b4f
1 in β†’ 1 out8.6200 XPM109 B
ANCZAhFA…4XJ8NSvi
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.

1.182 Γ— 10⁹⁢(97-digit number)
11826481566179740730…66444618012344730371
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
1.182 Γ— 10⁹⁢(97-digit number)
11826481566179740730…66444618012344730371
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.365 Γ— 10⁹⁢(97-digit number)
23652963132359481460…32889236024689460741
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.730 Γ— 10⁹⁢(97-digit number)
47305926264718962920…65778472049378921481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.461 Γ— 10⁹⁢(97-digit number)
94611852529437925841…31556944098757842961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.892 Γ— 10⁹⁷(98-digit number)
18922370505887585168…63113888197515685921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.784 Γ— 10⁹⁷(98-digit number)
37844741011775170336…26227776395031371841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.568 Γ— 10⁹⁷(98-digit number)
75689482023550340673…52455552790062743681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.513 Γ— 10⁹⁸(99-digit number)
15137896404710068134…04911105580125487361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.027 Γ— 10⁹⁸(99-digit number)
30275792809420136269…09822211160250974721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.055 Γ— 10⁹⁸(99-digit number)
60551585618840272538…19644422320501949441
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:57,704,992 XPMΒ·at block #6,807,619 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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