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Block #214,020

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/17/2013, 5:38:52 AM Β· Difficulty 9.9226 Β· 6,591,878 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
32d0f8cc3558e7ac4bbc1c5829f47f62e036e6d56eaa1fee632c627db136dd35
View on Chainz β†—

Height

#214,020

Difficulty

9.922642

Transactions

1

Size

208 B

Version

2

Bits

09ec3242

Nonce

16,778,156

Timestamp

10/17/2013, 5:38:52 AM

Confirmations

6,591,878

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

25470ba15e5088fe7d63dc3ba70dbf75de70282a65b3052781aa32eb57d07cbd
Transactions (1)
Coinbase25470ba15e5088…aa32eb57d07cbd
1 in β†’ 1 out10.1400 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.278 Γ— 10⁹⁹(100-digit number)
42781866447432667888…65813786840152191999
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
4.278 Γ— 10⁹⁹(100-digit number)
42781866447432667888…65813786840152191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.556 Γ— 10⁹⁹(100-digit number)
85563732894865335776…31627573680304383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.711 Γ— 10¹⁰⁰(101-digit number)
17112746578973067155…63255147360608767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.422 Γ— 10¹⁰⁰(101-digit number)
34225493157946134310…26510294721217535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.845 Γ— 10¹⁰⁰(101-digit number)
68450986315892268620…53020589442435071999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.369 Γ— 10¹⁰¹(102-digit number)
13690197263178453724…06041178884870143999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.738 Γ— 10¹⁰¹(102-digit number)
27380394526356907448…12082357769740287999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.476 Γ— 10¹⁰¹(102-digit number)
54760789052713814896…24164715539480575999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.095 Γ— 10¹⁰²(103-digit number)
10952157810542762979…48329431078961151999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,691,271 XPMΒ·at block #6,805,897 Β· updates every 60s
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