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Block #1,090,948

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/5/2015, 3:06:17 PM Β· Difficulty 10.7355 Β· 5,719,680 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6100737558c1e715702d3acfd34df30983b4f36c7069657690619cdfa84d27b8
View on Chainz β†—

Height

#1,090,948

Difficulty

10.735488

Transactions

1

Size

200 B

Version

2

Bits

0abc48ee

Nonce

11,673,793

Timestamp

6/5/2015, 3:06:17 PM

Confirmations

5,719,680

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

bd9ebee674a85d567c93e4a6760ad6d707b3ebc3dc89e2e27795ff6b6bc11240
Transactions (1)
Coinbasebd9ebee674a85d…95ff6b6bc11240
1 in β†’ 1 out8.6600 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.

3.750 Γ— 10⁹⁢(97-digit number)
37503843711795424573…81299713028121708561
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
3.750 Γ— 10⁹⁢(97-digit number)
37503843711795424573…81299713028121708561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.500 Γ— 10⁹⁢(97-digit number)
75007687423590849147…62599426056243417121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.500 Γ— 10⁹⁷(98-digit number)
15001537484718169829…25198852112486834241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.000 Γ— 10⁹⁷(98-digit number)
30003074969436339658…50397704224973668481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.000 Γ— 10⁹⁷(98-digit number)
60006149938872679317…00795408449947336961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.200 Γ— 10⁹⁸(99-digit number)
12001229987774535863…01590816899894673921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.400 Γ— 10⁹⁸(99-digit number)
24002459975549071727…03181633799789347841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.800 Γ— 10⁹⁸(99-digit number)
48004919951098143454…06363267599578695681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.600 Γ— 10⁹⁸(99-digit number)
96009839902196286908…12726535199157391361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.920 Γ— 10⁹⁹(100-digit number)
19201967980439257381…25453070398314782721
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:57,729,110 XPMΒ·at block #6,810,627 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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