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Block #1,606,511

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/30/2016, 10:07:09 AM Β· Difficulty 10.6071 Β· 5,230,468 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e14c9ee96d548be4e09e60f21b296f61339c9419dcb220359fc2fe354feab1c9
View on Chainz β†—

Height

#1,606,511

Difficulty

10.607077

Transactions

1

Size

199 B

Version

2

Bits

0a9b6969

Nonce

90,939,404

Timestamp

5/30/2016, 10:07:09 AM

Confirmations

5,230,468

Mined by

⛏️ P2SHAZfrqkykvp2kGUnKFHzUZCZqK86GGxxTHR

Merkle Root

4a2746e07f430cc4e15846eee3d94e5a12b61a6c23c7fbf87d2a4a30f41acf1b
Transactions (1)
Coinbase4a2746e07f430c…2a4a30f41acf1b
1 in β†’ 1 out8.8700 XPM110 B
AZfrqkyk…6GGxxTHR
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.

1.102 Γ— 10⁹²(93-digit number)
11023121279103582562…68065102472701690259
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
1.102 Γ— 10⁹²(93-digit number)
11023121279103582562…68065102472701690259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.204 Γ— 10⁹²(93-digit number)
22046242558207165125…36130204945403380519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.409 Γ— 10⁹²(93-digit number)
44092485116414330250…72260409890806761039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.818 Γ— 10⁹²(93-digit number)
88184970232828660500…44520819781613522079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.763 Γ— 10⁹³(94-digit number)
17636994046565732100…89041639563227044159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.527 Γ— 10⁹³(94-digit number)
35273988093131464200…78083279126454088319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.054 Γ— 10⁹³(94-digit number)
70547976186262928400…56166558252908176639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.410 Γ— 10⁹⁴(95-digit number)
14109595237252585680…12333116505816353279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.821 Γ— 10⁹⁴(95-digit number)
28219190474505171360…24666233011632706559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.643 Γ— 10⁹⁴(95-digit number)
56438380949010342720…49332466023265413119
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:57,940,131 XPMΒ·at block #6,836,978 Β· updates every 60s
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