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Block #2,656,595

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/11/2018, 5:09:20 AM Β· Difficulty 11.6874 Β· 4,188,262 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f705461c9c21895bcef5486bbeff27470e1bdf069e7f3b0da4c35eae7ef7f67c
View on Chainz β†—

Height

#2,656,595

Difficulty

11.687372

Transactions

2

Size

1.12 KB

Version

2

Bits

0baff7a1

Nonce

444,922,081

Timestamp

5/11/2018, 5:09:20 AM

Confirmations

4,188,262

Mined by

⛏️ P2SHAQvkG2t9MQh6YLnJrJerT7fbrbyTSf5sP8

Merkle Root

0762823d96e0e41338339429da0ea256e2064a999af7fef4af287f624372f8a2
Transactions (2)
Coinbasefceb824c4e8a67…601a996d5de871
1 in β†’ 1 out7.3200 XPM110 B
AQvkG2t9…yTSf5sP8
db8da5cdb50f79…032ffccc1d40e0
7 in β†’ 2 out40.1856 XPM942 B
ALxY52DP…ddHCywqXANWdJ2nc…BW7RisDk
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.

1.565 Γ— 10⁹⁴(95-digit number)
15654879440444080029…82448756097666410399
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
1.565 Γ— 10⁹⁴(95-digit number)
15654879440444080029…82448756097666410399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.130 Γ— 10⁹⁴(95-digit number)
31309758880888160058…64897512195332820799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.261 Γ— 10⁹⁴(95-digit number)
62619517761776320117…29795024390665641599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.252 Γ— 10⁹⁡(96-digit number)
12523903552355264023…59590048781331283199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.504 Γ— 10⁹⁡(96-digit number)
25047807104710528047…19180097562662566399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.009 Γ— 10⁹⁡(96-digit number)
50095614209421056094…38360195125325132799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.001 Γ— 10⁹⁢(97-digit number)
10019122841884211218…76720390250650265599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.003 Γ— 10⁹⁢(97-digit number)
20038245683768422437…53440780501300531199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.007 Γ— 10⁹⁢(97-digit number)
40076491367536844875…06881561002601062399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.015 Γ— 10⁹⁢(97-digit number)
80152982735073689750…13763122005202124799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.603 Γ— 10⁹⁷(98-digit number)
16030596547014737950…27526244010404249599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:58,003,268 XPMΒ·at block #6,844,856 Β· updates every 60s
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