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Block #1,416,131

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/16/2016, 7:30:00 PM Β· Difficulty 10.7970 Β· 5,422,709 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5b6f9c229da07c4303f83f7df8cde3d136b1929166a08df7c7dc8c95d65288df
View on Chainz β†—

Height

#1,416,131

Difficulty

10.796961

Transactions

1

Size

199 B

Version

2

Bits

0acc05a0

Nonce

75,094,044

Timestamp

1/16/2016, 7:30:00 PM

Confirmations

5,422,709

Mined by

⛏️ P2SHAekEzzXzVzVAPru1vkF7mHtMtok5EhfmZs

Merkle Root

5cb6c6075785331f9826dc1107187c383883c74d11946145d765cd6d4830639d
Transactions (1)
Coinbase5cb6c607578533…65cd6d4830639d
1 in β†’ 1 out8.5600 XPM109 B
AekEzzXz…k5EhfmZs
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.

2.456 Γ— 10⁹⁡(96-digit number)
24560322540444766625…30723452955160663039
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
2.456 Γ— 10⁹⁡(96-digit number)
24560322540444766625…30723452955160663039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.912 Γ— 10⁹⁡(96-digit number)
49120645080889533250…61446905910321326079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.824 Γ— 10⁹⁡(96-digit number)
98241290161779066501…22893811820642652159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.964 Γ— 10⁹⁢(97-digit number)
19648258032355813300…45787623641285304319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.929 Γ— 10⁹⁢(97-digit number)
39296516064711626600…91575247282570608639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.859 Γ— 10⁹⁢(97-digit number)
78593032129423253201…83150494565141217279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.571 Γ— 10⁹⁷(98-digit number)
15718606425884650640…66300989130282434559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.143 Γ— 10⁹⁷(98-digit number)
31437212851769301280…32601978260564869119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.287 Γ— 10⁹⁷(98-digit number)
62874425703538602560…65203956521129738239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.257 Γ— 10⁹⁸(99-digit number)
12574885140707720512…30407913042259476479
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:57,954,982 XPMΒ·at block #6,838,839 Β· updates every 60s
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