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Block #2,573,262

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/19/2018, 1:24:26 AM Β· Difficulty 10.9951 Β· 4,267,253 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
86c46d531981fd070e49df1fe3179ee503ef8b5d9c0b92b929e5f28692a386fb
View on Chainz β†—

Height

#2,573,262

Difficulty

10.995074

Transactions

2

Size

24.52 KB

Version

2

Bits

0afebd2e

Nonce

1,439,305,076

Timestamp

3/19/2018, 1:24:26 AM

Confirmations

4,267,253

Mined by

⛏️ P2SHAHJiTGSLcZtPq9VXsMk2HTrAAeiMobwNJ7

Merkle Root

48a953a5afb06865644d2e5ce34293c02c7b0eea1d588b0a9417c62df22f57b2
Transactions (2)
Coinbase0901fc7b05ff8c…6107d520de3459
1 in β†’ 1 out8.5600 XPM110 B
AHJiTGSL…iMobwNJ7
4725d568a2477b…dd58a9e4037c08
168 in β†’ 1 out5000.0000 XPM24.32 KB
ALPF8J52…Hjw4BMsG
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.

8.670 Γ— 10⁹²(93-digit number)
86703357561119390264…60598737552662354879
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
8.670 Γ— 10⁹²(93-digit number)
86703357561119390264…60598737552662354879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.734 Γ— 10⁹³(94-digit number)
17340671512223878052…21197475105324709759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.468 Γ— 10⁹³(94-digit number)
34681343024447756105…42394950210649419519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.936 Γ— 10⁹³(94-digit number)
69362686048895512211…84789900421298839039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.387 Γ— 10⁹⁴(95-digit number)
13872537209779102442…69579800842597678079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.774 Γ— 10⁹⁴(95-digit number)
27745074419558204884…39159601685195356159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.549 Γ— 10⁹⁴(95-digit number)
55490148839116409768…78319203370390712319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.109 Γ— 10⁹⁡(96-digit number)
11098029767823281953…56638406740781424639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.219 Γ— 10⁹⁡(96-digit number)
22196059535646563907…13276813481562849279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.439 Γ— 10⁹⁡(96-digit number)
44392119071293127815…26553626963125698559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.878 Γ— 10⁹⁡(96-digit number)
88784238142586255630…53107253926251397119
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:57,968,448 XPMΒ·at block #6,840,514 Β· updates every 60s
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