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Block #2,293,011

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/12/2017, 5:15:33 AM Β· Difficulty 10.9546 Β· 4,548,908 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
45569c9a8e2a56abd075896c6c9bad167c2d76f91501fc531f652a4d2e35a4a0
View on Chainz β†—

Height

#2,293,011

Difficulty

10.954599

Transactions

2

Size

426 B

Version

2

Bits

0af4609f

Nonce

1,346,632,775

Timestamp

9/12/2017, 5:15:33 AM

Confirmations

4,548,908

Mined by

⛏️ P2SHAbsLZJ4PHbhB4d4c2UtRt8aCUAC8SQs21K

Merkle Root

981db230c57570cec8bb1b839fc9c7aacafdc8eaf9926435746a255b69fac644
Transactions (2)
Coinbase483bd847b77bdc…80f2b2a1278dbc
1 in β†’ 1 out8.3300 XPM110 B
AbsLZJ4P…C8SQs21K
e7d772d87683d7…b1f26ef317b7a3
1 in β†’ 2 out2969.9900 XPM226 B
ARaNCeSx…b8M3uhxYAS7Q4TK1…c3ZwV4S2
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.

1.290 Γ— 10⁹⁴(95-digit number)
12909084260910430490…60961814331312461599
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
1.290 Γ— 10⁹⁴(95-digit number)
12909084260910430490…60961814331312461599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.581 Γ— 10⁹⁴(95-digit number)
25818168521820860980…21923628662624923199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.163 Γ— 10⁹⁴(95-digit number)
51636337043641721961…43847257325249846399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.032 Γ— 10⁹⁡(96-digit number)
10327267408728344392…87694514650499692799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.065 Γ— 10⁹⁡(96-digit number)
20654534817456688784…75389029300999385599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.130 Γ— 10⁹⁡(96-digit number)
41309069634913377569…50778058601998771199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.261 Γ— 10⁹⁡(96-digit number)
82618139269826755138…01556117203997542399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.652 Γ— 10⁹⁢(97-digit number)
16523627853965351027…03112234407995084799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.304 Γ— 10⁹⁢(97-digit number)
33047255707930702055…06224468815990169599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.609 Γ— 10⁹⁢(97-digit number)
66094511415861404110…12448937631980339199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.321 Γ— 10⁹⁷(98-digit number)
13218902283172280822…24897875263960678399
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:57,979,728 XPMΒ·at block #6,841,918 Β· updates every 60s
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