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Block #2,166,327

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/18/2017, 7:40:14 PM Β· Difficulty 10.8981 Β· 4,651,153 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
148fae8be60ad8d5c4d3628f59ed5066c8d3430ec4233a4f6445ff33211018c5
View on Chainz β†—

Height

#2,166,327

Difficulty

10.898066

Transactions

2

Size

2.73 KB

Version

2

Bits

0ae5e7a3

Nonce

195,732,952

Timestamp

6/18/2017, 7:40:14 PM

Confirmations

4,651,153

Mined by

⛏️ P2SHAd5vBREP66da62MDg6QQGABs3a1g7SS7Jj

Merkle Root

35cf80c13ab1a692ac16b0ffc45e2be96a618fe972726adfc2239c4c483deb45
Transactions (2)
Coinbase195d4f44bf5fae…fa34a4bca293dc
1 in β†’ 1 out8.4900 XPM109 B
Ad5vBREP…1g7SS7Jj
9e9a63bac033d2…35975055266d12
17 in β†’ 2 out64.0264 XPM2.53 KB
AJfQJid4…QR325TvkAcv4Xvi9…omzyhgXo
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.

1.304 Γ— 10⁹⁴(95-digit number)
13042365499374192055…80037493014780701349
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
1.304 Γ— 10⁹⁴(95-digit number)
13042365499374192055…80037493014780701349
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.608 Γ— 10⁹⁴(95-digit number)
26084730998748384110…60074986029561402699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.216 Γ— 10⁹⁴(95-digit number)
52169461997496768221…20149972059122805399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.043 Γ— 10⁹⁡(96-digit number)
10433892399499353644…40299944118245610799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.086 Γ— 10⁹⁡(96-digit number)
20867784798998707288…80599888236491221599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.173 Γ— 10⁹⁡(96-digit number)
41735569597997414577…61199776472982443199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.347 Γ— 10⁹⁡(96-digit number)
83471139195994829154…22399552945964886399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.669 Γ— 10⁹⁢(97-digit number)
16694227839198965830…44799105891929772799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.338 Γ— 10⁹⁢(97-digit number)
33388455678397931661…89598211783859545599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.677 Γ— 10⁹⁢(97-digit number)
66776911356795863323…79196423567719091199
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:57,783,893 XPMΒ·at block #6,817,479 Β· updates every 60s
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