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Block #169,389

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/17/2013, 11:47:10 PM Β· Difficulty 9.8677 Β· 6,673,653 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0e5490d2de108433ff743b7aa1ef891d2b37b8e05328a4c2fda26b8045cbed5b
View on Chainz β†—

Height

#169,389

Difficulty

9.867656

Transactions

1

Size

197 B

Version

2

Bits

09de1eae

Nonce

100,833

Timestamp

9/17/2013, 11:47:10 PM

Confirmations

6,673,653

Mined by

⛏️ P2SHAYAZW9zaEPqgug8XGBA3iA2Nf3da8AvwiQ

Merkle Root

d423b1727bdba42fae270f50eb90c79b858175e475dd86f439ee75065b4e368d
Transactions (1)
Coinbased423b1727bdba4…ee75065b4e368d
1 in β†’ 1 out10.2500 XPM109 B
AYAZW9za…da8AvwiQ
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.

4.331 Γ— 10⁹⁰(91-digit number)
43319973097633626339…22846238674492038159
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
4.331 Γ— 10⁹⁰(91-digit number)
43319973097633626339…22846238674492038159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.663 Γ— 10⁹⁰(91-digit number)
86639946195267252679…45692477348984076319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.732 Γ— 10⁹¹(92-digit number)
17327989239053450535…91384954697968152639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.465 Γ— 10⁹¹(92-digit number)
34655978478106901071…82769909395936305279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.931 Γ— 10⁹¹(92-digit number)
69311956956213802143…65539818791872610559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.386 Γ— 10⁹²(93-digit number)
13862391391242760428…31079637583745221119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.772 Γ— 10⁹²(93-digit number)
27724782782485520857…62159275167490442239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.544 Γ— 10⁹²(93-digit number)
55449565564971041714…24318550334980884479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.108 Γ— 10⁹³(94-digit number)
11089913112994208342…48637100669961768959
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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