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Block #2,051,476

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/3/2017, 1:04:12 PM Β· Difficulty 10.7150 Β· 4,789,169 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
82090cbe638b867029675be3a45091f795ae9f76848b6f94ac709acddbb8bed5
View on Chainz β†—

Height

#2,051,476

Difficulty

10.715012

Transactions

1

Size

199 B

Version

2

Bits

0ab70b01

Nonce

1,040,448,976

Timestamp

4/3/2017, 1:04:12 PM

Confirmations

4,789,169

Mined by

⛏️ P2SHAJfAxZKBkST7XQEgxw2WqduWfe4wowWfko

Merkle Root

f214141389e74e69b0fac830ccaf483d752be0ca91ef597d9dfd5a3c3c452dc9
Transactions (1)
Coinbasef214141389e74e…fd5a3c3c452dc9
1 in β†’ 1 out8.7000 XPM109 B
AJfAxZKB…4wowWfko
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.

2.879 Γ— 10⁹⁡(96-digit number)
28795478475985657317…94293313500607910721
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
2.879 Γ— 10⁹⁡(96-digit number)
28795478475985657317…94293313500607910721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.759 Γ— 10⁹⁡(96-digit number)
57590956951971314635…88586627001215821441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.151 Γ— 10⁹⁢(97-digit number)
11518191390394262927…77173254002431642881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.303 Γ— 10⁹⁢(97-digit number)
23036382780788525854…54346508004863285761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.607 Γ— 10⁹⁢(97-digit number)
46072765561577051708…08693016009726571521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.214 Γ— 10⁹⁢(97-digit number)
92145531123154103416…17386032019453143041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.842 Γ— 10⁹⁷(98-digit number)
18429106224630820683…34772064038906286081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.685 Γ— 10⁹⁷(98-digit number)
36858212449261641366…69544128077812572161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.371 Γ— 10⁹⁷(98-digit number)
73716424898523282733…39088256155625144321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.474 Γ— 10⁹⁸(99-digit number)
14743284979704656546…78176512311250288641
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:57,969,502 XPMΒ·at block #6,840,644 Β· updates every 60s
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