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Block #110,872

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/11/2013, 4:32:29 AM Β· Difficulty 9.6981 Β· 6,697,190 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
42005e3b5e18dc34362d51af25741e308c1257d36d0ac326375265ae46eab34c
View on Chainz β†—

Height

#110,872

Difficulty

9.698058

Transactions

2

Size

357 B

Version

2

Bits

09b2b3f1

Nonce

150,445

Timestamp

8/11/2013, 4:32:29 AM

Confirmations

6,697,190

Mined by

⛏️ P2SHAexpysrRoLesWgAzJw9ENujfsYg6WDnMqM

Merkle Root

e839ea10aed0fdc5da9b6261c44e383dc574334f62ccbd78469da349dc1968a6
Transactions (2)
Coinbaseb8cb7eac98aa4b…c58966daefc714
1 in β†’ 1 out10.6300 XPM109 B
AexpysrR…g6WDnMqM
6ee5e3a73d0021…561f70653dd70b
1 in β†’ 1 out10.8500 XPM158 B
AXkGUvU8…3ZLG8EHC
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.

4.652 Γ— 10⁹⁴(95-digit number)
46522382670349787126…18892267675748639429
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
4.652 Γ— 10⁹⁴(95-digit number)
46522382670349787126…18892267675748639429
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.304 Γ— 10⁹⁴(95-digit number)
93044765340699574253…37784535351497278859
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.860 Γ— 10⁹⁡(96-digit number)
18608953068139914850…75569070702994557719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.721 Γ— 10⁹⁡(96-digit number)
37217906136279829701…51138141405989115439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.443 Γ— 10⁹⁡(96-digit number)
74435812272559659402…02276282811978230879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.488 Γ— 10⁹⁢(97-digit number)
14887162454511931880…04552565623956461759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.977 Γ— 10⁹⁢(97-digit number)
29774324909023863761…09105131247912923519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.954 Γ— 10⁹⁢(97-digit number)
59548649818047727522…18210262495825847039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.190 Γ— 10⁹⁷(98-digit number)
11909729963609545504…36420524991651694079
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:57,708,540 XPMΒ·at block #6,808,061 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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