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Block #3,505,428

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/8/2020, 3:11:34 PM Β· Difficulty 10.9303 Β· 3,331,266 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5c92a8a02cd2dd38ae731a16974af8c91e1fa49051ddfc3ba984e7527f42118d
View on Chainz β†—

Height

#3,505,428

Difficulty

10.930333

Transactions

2

Size

7.47 KB

Version

2

Bits

0aee2a4e

Nonce

143,966,652

Timestamp

1/8/2020, 3:11:34 PM

Confirmations

3,331,266

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

8e87bf1728bed1914cf728306f71f2c1b7fa273aa4753528275293b4246652a8
Transactions (2)
Coinbase30fd47c1eb91ee…7e6c3524b5efaa
1 in β†’ 1 out8.4400 XPM110 B
ASiq2qtK…VMhmk7yL
ab88eb6e27998e…79c7952cc5699e
50 in β†’ 1 out199.9200 XPM7.27 KB
ALcTQaSP…1C5Yf2Zi
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.

3.355 Γ— 10⁹⁴(95-digit number)
33553377731127784673…41175317970427497409
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
3.355 Γ— 10⁹⁴(95-digit number)
33553377731127784673…41175317970427497409
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.710 Γ— 10⁹⁴(95-digit number)
67106755462255569347…82350635940854994819
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.342 Γ— 10⁹⁡(96-digit number)
13421351092451113869…64701271881709989639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.684 Γ— 10⁹⁡(96-digit number)
26842702184902227739…29402543763419979279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.368 Γ— 10⁹⁡(96-digit number)
53685404369804455478…58805087526839958559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.073 Γ— 10⁹⁢(97-digit number)
10737080873960891095…17610175053679917119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.147 Γ— 10⁹⁢(97-digit number)
21474161747921782191…35220350107359834239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.294 Γ— 10⁹⁢(97-digit number)
42948323495843564382…70440700214719668479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.589 Γ— 10⁹⁢(97-digit number)
85896646991687128765…40881400429439336959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.717 Γ— 10⁹⁷(98-digit number)
17179329398337425753…81762800858878673919
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:57,937,832 XPMΒ·at block #6,836,693 Β· updates every 60s
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