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Block #1,860,853

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/22/2016, 7:56:20 AM Β· Difficulty 10.6912 Β· 4,972,360 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5f0f5bfb1b4c40a4674fe49d31b8dd8c24d65dff040915b60e2ece56b1d8a2c2
View on Chainz β†—

Height

#1,860,853

Difficulty

10.691175

Transactions

2

Size

869 B

Version

2

Bits

0ab0f0dc

Nonce

766,178,389

Timestamp

11/22/2016, 7:56:20 AM

Confirmations

4,972,360

Mined by

⛏️ P2SHAMRFJ2jTEnB9oSjJrLwYtrrBkhJkLe9z3p

Merkle Root

5521e0c2789f74859933d54cc93e77749761f0de0777f3215d3511dde63445aa
Transactions (2)
Coinbaseb3b9ab50330f4d…c61cab2bab9605
1 in β†’ 1 out8.7500 XPM110 B
AMRFJ2jT…JkLe9z3p
79887b56bb6134…c23f52789f372f
4 in β†’ 2 out1.3812 XPM669 B
ATwNKBPa…YJ2cGqj6AQubDEq3…xR53mZQk
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.

5.081 Γ— 10⁹³(94-digit number)
50810195730679127804…96418466985375362559
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
5.081 Γ— 10⁹³(94-digit number)
50810195730679127804…96418466985375362559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.016 Γ— 10⁹⁴(95-digit number)
10162039146135825560…92836933970750725119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.032 Γ— 10⁹⁴(95-digit number)
20324078292271651121…85673867941501450239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.064 Γ— 10⁹⁴(95-digit number)
40648156584543302243…71347735883002900479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.129 Γ— 10⁹⁴(95-digit number)
81296313169086604487…42695471766005800959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.625 Γ— 10⁹⁡(96-digit number)
16259262633817320897…85390943532011601919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.251 Γ— 10⁹⁡(96-digit number)
32518525267634641795…70781887064023203839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.503 Γ— 10⁹⁡(96-digit number)
65037050535269283590…41563774128046407679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.300 Γ— 10⁹⁢(97-digit number)
13007410107053856718…83127548256092815359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.601 Γ— 10⁹⁢(97-digit number)
26014820214107713436…66255096512185630719
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:57,909,890 XPMΒ·at block #6,833,212 Β· updates every 60s
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