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Block #166,060

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/15/2013, 4:43:04 PM Β· Difficulty 9.8668 Β· 6,638,240 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d795ee3b603259672f38cf163cb87f533b436fa95749db02e3f13f0ed4a32214
View on Chainz β†—

Height

#166,060

Difficulty

9.866840

Transactions

2

Size

1016 B

Version

2

Bits

09dde934

Nonce

4,647

Timestamp

9/15/2013, 4:43:04 PM

Confirmations

6,638,240

Mined by

⛏️ P2SHAGtiYkzRzPqqXVAsPkt4YctCi6Xq14yS4j

Merkle Root

45b45dceafc98f0677382214e8789c78f97b45206eca338ced21fd0fd487271d
Transactions (2)
Coinbaseaaaaceba7336b6…4d6e0180f325bb
1 in β†’ 1 out10.2700 XPM109 B
AGtiYkzR…Xq14yS4j
6eef3842e0d564…ba5d3fed6ea82a
5 in β†’ 2 out25.6494 XPM817 B
ASZHg2HY…bn3BvdBAAXbYUW9A…tn8jzxwA
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.

1.646 Γ— 10⁹⁴(95-digit number)
16464934504370837982…76598876357199201649
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
1.646 Γ— 10⁹⁴(95-digit number)
16464934504370837982…76598876357199201649
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.292 Γ— 10⁹⁴(95-digit number)
32929869008741675965…53197752714398403299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.585 Γ— 10⁹⁴(95-digit number)
65859738017483351930…06395505428796806599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.317 Γ— 10⁹⁡(96-digit number)
13171947603496670386…12791010857593613199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.634 Γ— 10⁹⁡(96-digit number)
26343895206993340772…25582021715187226399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.268 Γ— 10⁹⁡(96-digit number)
52687790413986681544…51164043430374452799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.053 Γ— 10⁹⁢(97-digit number)
10537558082797336308…02328086860748905599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.107 Γ— 10⁹⁢(97-digit number)
21075116165594672617…04656173721497811199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.215 Γ— 10⁹⁢(97-digit number)
42150232331189345235…09312347442995622399
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:57,678,459 XPMΒ·at block #6,804,299 Β· updates every 60s
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