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Block #4,564,361

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/16/2022, 7:04:28 PM Β· Difficulty 10.8387 Β· 2,245,972 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
09e7f0bd3b6ba99b4fcca17c3ce7c9189df7c8c1b1071aee8d7741f000be0ada
View on Chainz β†—

Height

#4,564,361

Difficulty

10.838657

Transactions

2

Size

4.71 KB

Version

2

Bits

0ad6b239

Nonce

1,656,543,885

Timestamp

1/16/2022, 7:04:28 PM

Confirmations

2,245,972

Mined by

⛏️ xpmforall.orgAXfJqzUb1MbPSQVbWWFibnVbwWHXeXmjMzVisit pool β†—

Merkle Root

45c8539bf69f7cbb121044fda1828e0613389dfd923750f646357dc57c4fbc99
Transactions (2)
Coinbase3b81e03dc4f5a8…043ff04a6e6f2b
1 in β†’ 1 out8.5500 XPM109 B
AXfJqzUb…HXeXmjMz
ceefd0245a4f54…404902d82e1f8a
31 in β†’ 1 out290.5817 XPM4.52 KB
Ac7AHdWA…VW9SxsN4
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.

3.030 Γ— 10⁹⁡(96-digit number)
30303479814933857992…35652648516799733759
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
3.030 Γ— 10⁹⁡(96-digit number)
30303479814933857992…35652648516799733759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.060 Γ— 10⁹⁡(96-digit number)
60606959629867715985…71305297033599467519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.212 Γ— 10⁹⁢(97-digit number)
12121391925973543197…42610594067198935039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.424 Γ— 10⁹⁢(97-digit number)
24242783851947086394…85221188134397870079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.848 Γ— 10⁹⁢(97-digit number)
48485567703894172788…70442376268795740159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.697 Γ— 10⁹⁢(97-digit number)
96971135407788345576…40884752537591480319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.939 Γ— 10⁹⁷(98-digit number)
19394227081557669115…81769505075182960639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.878 Γ— 10⁹⁷(98-digit number)
38788454163115338230…63539010150365921279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.757 Γ— 10⁹⁷(98-digit number)
77576908326230676460…27078020300731842559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.551 Γ— 10⁹⁸(99-digit number)
15515381665246135292…54156040601463685119
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:57,726,744 XPMΒ·at block #6,810,332 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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