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Block #1,404,580

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/8/2016, 3:17:57 PM Β· Difficulty 10.8053 Β· 5,438,201 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
52f9cb7328c6e7906134ef9ebd0aea64158211c8a402802c89449f37b529a8d9
View on Chainz β†—

Height

#1,404,580

Difficulty

10.805319

Transactions

1

Size

201 B

Version

2

Bits

0ace295e

Nonce

1,634,860,449

Timestamp

1/8/2016, 3:17:57 PM

Confirmations

5,438,201

Mined by

⛏️ P2SHAKiitFSWxcnmoN32bMjEH9qnP95CpLP8wN

Merkle Root

caf50898641cd60a978e87b700803aa141d59896d3e457fb1220f51921385c2f
Transactions (1)
Coinbasecaf50898641cd6…20f51921385c2f
1 in β†’ 1 out8.5500 XPM110 B
AKiitFSW…5CpLP8wN
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.

1.748 Γ— 10⁹⁢(97-digit number)
17486593269873739645…53189529255169087999
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
1.748 Γ— 10⁹⁢(97-digit number)
17486593269873739645…53189529255169087999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.497 Γ— 10⁹⁢(97-digit number)
34973186539747479291…06379058510338175999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.994 Γ— 10⁹⁢(97-digit number)
69946373079494958583…12758117020676351999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.398 Γ— 10⁹⁷(98-digit number)
13989274615898991716…25516234041352703999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.797 Γ— 10⁹⁷(98-digit number)
27978549231797983433…51032468082705407999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.595 Γ— 10⁹⁷(98-digit number)
55957098463595966866…02064936165410815999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.119 Γ— 10⁹⁸(99-digit number)
11191419692719193373…04129872330821631999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.238 Γ— 10⁹⁸(99-digit number)
22382839385438386746…08259744661643263999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.476 Γ— 10⁹⁸(99-digit number)
44765678770876773493…16519489323286527999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.953 Γ— 10⁹⁸(99-digit number)
89531357541753546986…33038978646573055999
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:57,986,587 XPMΒ·at block #6,842,780 Β· updates every 60s
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