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Block #113,348

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/12/2013, 11:55:30 AM Β· Difficulty 9.7317 Β· 6,703,291 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
58a413bcbb3f8ae6ac2fdb3800e13535e4eae636af9b3d30ffb626af39c7a553
View on Chainz β†—

Height

#113,348

Difficulty

9.731702

Transactions

2

Size

359 B

Version

2

Bits

09bb50da

Nonce

13,626

Timestamp

8/12/2013, 11:55:30 AM

Confirmations

6,703,291

Mined by

⛏️ P2SHAVLgKQnAVKgFjikWfmntHAVPY47QaAsNtd

Merkle Root

c6deda21e332f72a76a3ab153d0db4ef5091c2c3e620763e104f633cc954eae8
Transactions (2)
Coinbaseec1a05dd17f527…2f95d82120b1d2
1 in β†’ 1 out10.5500 XPM109 B
AVLgKQnA…7QaAsNtd
0b21d11bc2a72c…40296fb5b7b666
1 in β†’ 1 out10.6300 XPM158 B
AQj5CF31…Sfv2KzXY
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.

2.632 Γ— 10⁹⁸(99-digit number)
26329342587356802291…73001549423386977639
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
2.632 Γ— 10⁹⁸(99-digit number)
26329342587356802291…73001549423386977639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.265 Γ— 10⁹⁸(99-digit number)
52658685174713604583…46003098846773955279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.053 Γ— 10⁹⁹(100-digit number)
10531737034942720916…92006197693547910559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.106 Γ— 10⁹⁹(100-digit number)
21063474069885441833…84012395387095821119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.212 Γ— 10⁹⁹(100-digit number)
42126948139770883666…68024790774191642239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.425 Γ— 10⁹⁹(100-digit number)
84253896279541767333…36049581548383284479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.685 Γ— 10¹⁰⁰(101-digit number)
16850779255908353466…72099163096766568959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.370 Γ— 10¹⁰⁰(101-digit number)
33701558511816706933…44198326193533137919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.740 Γ— 10¹⁰⁰(101-digit number)
67403117023633413866…88396652387066275839
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:57,777,228 XPMΒ·at block #6,816,638 Β· updates every 60s
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