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Block #2,094,431

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2017, 2:41:02 PM Β· Difficulty 10.8721 Β· 4,748,047 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d6970c9f8825c179702125f96c570b05e71cf206d17b209235527a344f28b86e
View on Chainz β†—

Height

#2,094,431

Difficulty

10.872054

Transactions

2

Size

1.66 KB

Version

2

Bits

0adf3ef6

Nonce

253,700,670

Timestamp

4/30/2017, 2:41:02 PM

Confirmations

4,748,047

Mined by

⛏️ P2SHARN2ohrqvCG9dqotzXwsyf4Cz47LYYQg6j

Merkle Root

44b6d7e60fa00689b392a38d92643ea7b8fb5aef0fc701dbe15d0eaf509693ba
Transactions (2)
Coinbase6fce5128e65510…644e97678ec07e
1 in β†’ 1 out8.4700 XPM110 B
ARN2ohrq…7LYYQg6j
2694c972b5d944…a4363710f999b5
11 in β†’ 2 out54.1273 XPM1.47 KB
AMLiyYLv…iYQLf2JUAHELiiq5…24QbCF1T
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.

1.259 Γ— 10⁹⁡(96-digit number)
12595593671204659325…36883187066348396959
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
1.259 Γ— 10⁹⁡(96-digit number)
12595593671204659325…36883187066348396959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.519 Γ— 10⁹⁡(96-digit number)
25191187342409318650…73766374132696793919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.038 Γ— 10⁹⁡(96-digit number)
50382374684818637301…47532748265393587839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.007 Γ— 10⁹⁢(97-digit number)
10076474936963727460…95065496530787175679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.015 Γ— 10⁹⁢(97-digit number)
20152949873927454920…90130993061574351359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.030 Γ— 10⁹⁢(97-digit number)
40305899747854909840…80261986123148702719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.061 Γ— 10⁹⁢(97-digit number)
80611799495709819681…60523972246297405439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.612 Γ— 10⁹⁷(98-digit number)
16122359899141963936…21047944492594810879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.224 Γ— 10⁹⁷(98-digit number)
32244719798283927872…42095888985189621759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.448 Γ— 10⁹⁷(98-digit number)
64489439596567855745…84191777970379243519
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:57,984,241 XPMΒ·at block #6,842,477 Β· updates every 60s
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