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Block #2,051,412

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2017, 12:30:20 PM Β· Difficulty 10.7133 Β· 4,790,802 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c16bed55bfbe27587b20bbc2634840cc12e08f4dc4bcce2f855fb89b5a9cf088
View on Chainz β†—

Height

#2,051,412

Difficulty

10.713337

Transactions

1

Size

200 B

Version

2

Bits

0ab69d3e

Nonce

1,547,910,163

Timestamp

4/3/2017, 12:30:20 PM

Confirmations

4,790,802

Mined by

⛏️ P2SHAJcLshy6VMeZrZdyTsfwKxUcWEFFZeJfCK

Merkle Root

4e01d8d78e85c2a633b4f2bcdd06a63405f53e540486dd9cfbd52f7feb58e742
Transactions (1)
Coinbase4e01d8d78e85c2…d52f7feb58e742
1 in β†’ 1 out8.7000 XPM110 B
AJcLshy6…FFZeJfCK
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.

6.101 Γ— 10⁹⁡(96-digit number)
61014580856920932139…60482168357714242559
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
6.101 Γ— 10⁹⁡(96-digit number)
61014580856920932139…60482168357714242559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.220 Γ— 10⁹⁢(97-digit number)
12202916171384186427…20964336715428485119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.440 Γ— 10⁹⁢(97-digit number)
24405832342768372855…41928673430856970239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.881 Γ— 10⁹⁢(97-digit number)
48811664685536745711…83857346861713940479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.762 Γ— 10⁹⁢(97-digit number)
97623329371073491423…67714693723427880959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.952 Γ— 10⁹⁷(98-digit number)
19524665874214698284…35429387446855761919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.904 Γ— 10⁹⁷(98-digit number)
39049331748429396569…70858774893711523839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.809 Γ— 10⁹⁷(98-digit number)
78098663496858793139…41717549787423047679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.561 Γ— 10⁹⁸(99-digit number)
15619732699371758627…83435099574846095359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.123 Γ— 10⁹⁸(99-digit number)
31239465398743517255…66870199149692190719
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,982,109 XPMΒ·at block #6,842,213 Β· updates every 60s
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