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Block #2,634,870

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 1:25:24 AM Β· Difficulty 11.2755 Β· 4,196,422 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a4328bee7328a9fd917a7835230228c9e3a8e6558748f037502139d3a8b41458
View on Chainz β†—

Height

#2,634,870

Difficulty

11.275463

Transactions

1

Size

201 B

Version

2

Bits

0b4684bd

Nonce

339,597,289

Timestamp

4/29/2018, 1:25:24 AM

Confirmations

4,196,422

Mined by

⛏️ P2SHAcqGzQnwZCNYgyaQqiwv11iSjdBhUJ8Jhm

Merkle Root

d5bd1c4dd9473849a225b566cce0854e907507a44ec508ae35eeb349f64a0d43
Transactions (1)
Coinbased5bd1c4dd94738…eeb349f64a0d43
1 in β†’ 1 out7.8500 XPM110 B
AcqGzQnw…BhUJ8Jhm
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.

1.901 Γ— 10⁹⁷(98-digit number)
19017531521663065231…04194084145065534721
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.901 Γ— 10⁹⁷(98-digit number)
19017531521663065231…04194084145065534721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.803 Γ— 10⁹⁷(98-digit number)
38035063043326130463…08388168290131069441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.607 Γ— 10⁹⁷(98-digit number)
76070126086652260927…16776336580262138881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.521 Γ— 10⁹⁸(99-digit number)
15214025217330452185…33552673160524277761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.042 Γ— 10⁹⁸(99-digit number)
30428050434660904370…67105346321048555521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.085 Γ— 10⁹⁸(99-digit number)
60856100869321808741…34210692642097111041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.217 Γ— 10⁹⁹(100-digit number)
12171220173864361748…68421385284194222081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.434 Γ— 10⁹⁹(100-digit number)
24342440347728723496…36842770568388444161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.868 Γ— 10⁹⁹(100-digit number)
48684880695457446993…73685541136776888321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.736 Γ— 10⁹⁹(100-digit number)
97369761390914893986…47371082273553776641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.947 Γ— 10¹⁰⁰(101-digit number)
19473952278182978797…94742164547107553281
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,894,482 XPMΒ·at block #6,831,291 Β· updates every 60s
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