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Block #2,478,855

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/18/2018, 1:31:52 PM Β· Difficulty 10.9657 Β· 4,365,647 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
08dcf5df71d7b7257d6b5eecfe3df27fa7926fdf84e907e4fb8761294f85343d
View on Chainz β†—

Height

#2,478,855

Difficulty

10.965681

Transactions

1

Size

200 B

Version

2

Bits

0af736e0

Nonce

1,715,505,578

Timestamp

1/18/2018, 1:31:52 PM

Confirmations

4,365,647

Mined by

⛏️ P2SHALzJB2iyHs6i1h8VyiFhS2uFvvbVEiFMv7

Merkle Root

4dc36bc7dcb7f151fdea911092631dbbcbade022122501f1d9557a9af18400d8
Transactions (1)
Coinbase4dc36bc7dcb7f1…557a9af18400d8
1 in β†’ 1 out8.3000 XPM110 B
ALzJB2iy…bVEiFMv7
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.

2.939 Γ— 10⁹⁡(96-digit number)
29394081590371335140…79788488745567987199
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
2.939 Γ— 10⁹⁡(96-digit number)
29394081590371335140…79788488745567987199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.878 Γ— 10⁹⁡(96-digit number)
58788163180742670280…59576977491135974399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.175 Γ— 10⁹⁢(97-digit number)
11757632636148534056…19153954982271948799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.351 Γ— 10⁹⁢(97-digit number)
23515265272297068112…38307909964543897599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.703 Γ— 10⁹⁢(97-digit number)
47030530544594136224…76615819929087795199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.406 Γ— 10⁹⁢(97-digit number)
94061061089188272449…53231639858175590399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.881 Γ— 10⁹⁷(98-digit number)
18812212217837654489…06463279716351180799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.762 Γ— 10⁹⁷(98-digit number)
37624424435675308979…12926559432702361599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.524 Γ— 10⁹⁷(98-digit number)
75248848871350617959…25853118865404723199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.504 Γ— 10⁹⁸(99-digit number)
15049769774270123591…51706237730809446399
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:58,000,413 XPMΒ·at block #6,844,501 Β· updates every 60s
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