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Block #2,847,269

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 9/20/2018, 3:29:41 AM Β· Difficulty 11.7328 Β· 3,997,233 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
214523ff57907403bb7fc81fd9d729e6c6f76fba8031962399a3bbb549963577
View on Chainz β†—

Height

#2,847,269

Difficulty

11.732764

Transactions

1

Size

200 B

Version

2

Bits

0bbb9673

Nonce

38,118,004

Timestamp

9/20/2018, 3:29:41 AM

Confirmations

3,997,233

Mined by

⛏️ P2SHAdc9DHCSNYtXcbwspcz2W4vcsUFtxfiDpS

Merkle Root

afefb6a105a8d58d0bd57963f7eb014dfeb99c158a232b5ab6bc0121caec1eb0
Transactions (1)
Coinbaseafefb6a105a8d5…bc0121caec1eb0
1 in β†’ 1 out7.2500 XPM109 B
Adc9DHCS…FtxfiDpS
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.

2.074 Γ— 10⁹⁷(98-digit number)
20741269880313203664…09694920652443832319
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
2.074 Γ— 10⁹⁷(98-digit number)
20741269880313203664…09694920652443832319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.148 Γ— 10⁹⁷(98-digit number)
41482539760626407329…19389841304887664639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.296 Γ— 10⁹⁷(98-digit number)
82965079521252814659…38779682609775329279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.659 Γ— 10⁹⁸(99-digit number)
16593015904250562931…77559365219550658559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.318 Γ— 10⁹⁸(99-digit number)
33186031808501125863…55118730439101317119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.637 Γ— 10⁹⁸(99-digit number)
66372063617002251727…10237460878202634239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.327 Γ— 10⁹⁹(100-digit number)
13274412723400450345…20474921756405268479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.654 Γ— 10⁹⁹(100-digit number)
26548825446800900690…40949843512810536959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.309 Γ— 10⁹⁹(100-digit number)
53097650893601801381…81899687025621073919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.061 Γ— 10¹⁰⁰(101-digit number)
10619530178720360276…63799374051242147839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.123 Γ— 10¹⁰⁰(101-digit number)
21239060357440720552…27598748102484295679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
4.247 Γ— 10¹⁰⁰(101-digit number)
42478120714881441105…55197496204968591359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:58,000,413 XPMΒ·at block #6,844,501 Β· updates every 60s
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