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Block #2,126,437

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/21/2017, 6:06:37 AM Β· Difficulty 10.9193 Β· 4,715,419 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9810d8926e9692cb2711ee23c519771520fd4f99d4c04bd8d0c4442326acac4b
View on Chainz β†—

Height

#2,126,437

Difficulty

10.919345

Transactions

1

Size

243 B

Version

2

Bits

0aeb5a38

Nonce

1,976,768,236

Timestamp

5/21/2017, 6:06:37 AM

Confirmations

4,715,419

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

84a2de6f8bc06176b5877d7e02c7e63b55f523aec1994700b2cb648d7e90df22
Transactions (1)
Coinbase84a2de6f8bc061…cb648d7e90df22
1 in β†’ 2 out8.3700 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

1.006 Γ— 10⁹⁢(97-digit number)
10061059920670569581…91693267409323740001
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
1.006 Γ— 10⁹⁢(97-digit number)
10061059920670569581…91693267409323740001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.012 Γ— 10⁹⁢(97-digit number)
20122119841341139162…83386534818647480001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.024 Γ— 10⁹⁢(97-digit number)
40244239682682278324…66773069637294960001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.048 Γ— 10⁹⁢(97-digit number)
80488479365364556649…33546139274589920001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.609 Γ— 10⁹⁷(98-digit number)
16097695873072911329…67092278549179840001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.219 Γ— 10⁹⁷(98-digit number)
32195391746145822659…34184557098359680001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.439 Γ— 10⁹⁷(98-digit number)
64390783492291645319…68369114196719360001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.287 Γ— 10⁹⁸(99-digit number)
12878156698458329063…36738228393438720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.575 Γ— 10⁹⁸(99-digit number)
25756313396916658127…73476456786877440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.151 Γ— 10⁹⁸(99-digit number)
51512626793833316255…46952913573754880001
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:57,979,224 XPMΒ·at block #6,841,855 Β· updates every 60s
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