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Block #211,288

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/15/2013, 3:36:12 PM Β· Difficulty 9.9153 Β· 6,605,135 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
89c901edc28ebdf893da2a4e97fc734e7f5df3d8db6b1d8f9a1b9ae9722f7e86
View on Chainz β†—

Height

#211,288

Difficulty

9.915260

Transactions

1

Size

198 B

Version

2

Bits

09ea4e7b

Nonce

1,579

Timestamp

10/15/2013, 3:36:12 PM

Confirmations

6,605,135

Mined by

⛏️ P2SHAHNdTz9RdyhMpsaRttP7HwiXvgDHU2jpcA

Merkle Root

4c692e4b48e4036b4b06c8b83bc6d8996736278354d51eccb7350d9f11bfae84
Transactions (1)
Coinbase4c692e4b48e403…350d9f11bfae84
1 in β†’ 1 out10.1600 XPM109 B
AHNdTz9R…DHU2jpcA
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.

2.328 Γ— 10⁹³(94-digit number)
23289429676901264408…34723614808450296319
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
2.328 Γ— 10⁹³(94-digit number)
23289429676901264408…34723614808450296319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.657 Γ— 10⁹³(94-digit number)
46578859353802528817…69447229616900592639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.315 Γ— 10⁹³(94-digit number)
93157718707605057634…38894459233801185279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.863 Γ— 10⁹⁴(95-digit number)
18631543741521011526…77788918467602370559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.726 Γ— 10⁹⁴(95-digit number)
37263087483042023053…55577836935204741119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.452 Γ— 10⁹⁴(95-digit number)
74526174966084046107…11155673870409482239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.490 Γ— 10⁹⁡(96-digit number)
14905234993216809221…22311347740818964479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.981 Γ— 10⁹⁡(96-digit number)
29810469986433618443…44622695481637928959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.962 Γ— 10⁹⁡(96-digit number)
59620939972867236886…89245390963275857919
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
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