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Block #2,925,450

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/16/2018, 1:13:11 PM Β· Difficulty 11.3545 Β· 3,917,474 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ac117f36cc14024b71270f90d896f9e759a67e28a70b69c48587741f976b7821
View on Chainz β†—

Height

#2,925,450

Difficulty

11.354522

Transactions

2

Size

7.47 KB

Version

2

Bits

0b5ac1fc

Nonce

437,412,080

Timestamp

11/16/2018, 1:13:11 PM

Confirmations

3,917,474

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

76319c1d3a9b73c7d33280bb8aeb7720637d8210ab35e036b3424d12c4229af0
Transactions (2)
Coinbaseaa241769b8b731…e43dff5f935f89
1 in β†’ 1 out7.8200 XPM110 B
AbXwmGxD…4XXYP765
37aa5922d73a2d…e5711267e2240a
50 in β†’ 1 out230.0938 XPM7.27 KB
AbF4i7B6…C1DHtmJN
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.

4.158 Γ— 10⁹⁢(97-digit number)
41584233400590040924…78037791925210410879
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
4.158 Γ— 10⁹⁢(97-digit number)
41584233400590040924…78037791925210410879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.316 Γ— 10⁹⁢(97-digit number)
83168466801180081849…56075583850420821759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.663 Γ— 10⁹⁷(98-digit number)
16633693360236016369…12151167700841643519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.326 Γ— 10⁹⁷(98-digit number)
33267386720472032739…24302335401683287039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.653 Γ— 10⁹⁷(98-digit number)
66534773440944065479…48604670803366574079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.330 Γ— 10⁹⁸(99-digit number)
13306954688188813095…97209341606733148159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.661 Γ— 10⁹⁸(99-digit number)
26613909376377626191…94418683213466296319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.322 Γ— 10⁹⁸(99-digit number)
53227818752755252383…88837366426932592639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.064 Γ— 10⁹⁹(100-digit number)
10645563750551050476…77674732853865185279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.129 Γ— 10⁹⁹(100-digit number)
21291127501102100953…55349465707730370559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.258 Γ— 10⁹⁹(100-digit number)
42582255002204201906…10698931415460741119
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:57,987,740 XPMΒ·at block #6,842,923 Β· updates every 60s
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