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Block #2,836,999

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/13/2018, 5:06:23 AM Β· Difficulty 11.7169 Β· 4,004,667 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dcf4cdc966b0eb46b34f390c4d87fe0dc8b306ec3ce88dd170aa9abcf1fd716b
View on Chainz β†—

Height

#2,836,999

Difficulty

11.716907

Transactions

2

Size

426 B

Version

2

Bits

0bb78732

Nonce

852,412,402

Timestamp

9/13/2018, 5:06:23 AM

Confirmations

4,004,667

Mined by

⛏️ P2SHAHH583P6HLJEPxdiF7buvZuH1v5uwRwasq

Merkle Root

411542c80ed3e880c70e6d0eb4e002f0b7f7e0236c2e3b9e181487cc4d7905ee
Transactions (2)
Coinbasee5fcdeec0f9ec4…880345b0efc8a6
1 in β†’ 1 out7.2800 XPM110 B
AHH583P6…5uwRwasq
49c41009d70323…dc738abf18e2d6
1 in β†’ 2 out1169.0490 XPM226 B
AJcDB81D…ZX2on3CsATbKrzB5…xzxyfPVM
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.

3.856 Γ— 10⁹³(94-digit number)
38560514992668229238…95980714198939559999
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
3.856 Γ— 10⁹³(94-digit number)
38560514992668229238…95980714198939559999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.712 Γ— 10⁹³(94-digit number)
77121029985336458477…91961428397879119999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.542 Γ— 10⁹⁴(95-digit number)
15424205997067291695…83922856795758239999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.084 Γ— 10⁹⁴(95-digit number)
30848411994134583391…67845713591516479999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.169 Γ— 10⁹⁴(95-digit number)
61696823988269166782…35691427183032959999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.233 Γ— 10⁹⁡(96-digit number)
12339364797653833356…71382854366065919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.467 Γ— 10⁹⁡(96-digit number)
24678729595307666712…42765708732131839999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.935 Γ— 10⁹⁡(96-digit number)
49357459190615333425…85531417464263679999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.871 Γ— 10⁹⁡(96-digit number)
98714918381230666851…71062834928527359999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.974 Γ— 10⁹⁢(97-digit number)
19742983676246133370…42125669857054719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.948 Γ— 10⁹⁢(97-digit number)
39485967352492266740…84251339714109439999
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:57,977,717 XPMΒ·at block #6,841,665 Β· updates every 60s
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