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Block #41,045

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 3:59:06 PM Β· Difficulty 8.4901 Β· 6,783,842 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7c9e79956b7c1ba9a55ccbeb990a2c2f2eb83db12ac74bcda2aa45947b83b125
View on Chainz β†—

Height

#41,045

Difficulty

8.490062

Transactions

1

Size

201 B

Version

2

Bits

087d74b9

Nonce

12

Timestamp

7/14/2013, 3:59:06 PM

Confirmations

6,783,842

Mined by

⛏️ P2SHAH1HZSAYsQMpsfvCMZqMsj4V3wmn5a28BR

Merkle Root

90ab45be8ec7bb9fc1fb5864fde9cc62b16ab9980e442af766326c5007c3fd6a
Transactions (1)
Coinbase90ab45be8ec7bb…326c5007c3fd6a
1 in β†’ 1 out13.8500 XPM110 B
AH1HZSAY…mn5a28BR
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.

3.590 Γ— 10⁹⁢(97-digit number)
35908868434940409582…36092217709039378799
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
3.590 Γ— 10⁹⁢(97-digit number)
35908868434940409582…36092217709039378799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.181 Γ— 10⁹⁢(97-digit number)
71817736869880819164…72184435418078757599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.436 Γ— 10⁹⁷(98-digit number)
14363547373976163832…44368870836157515199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.872 Γ— 10⁹⁷(98-digit number)
28727094747952327665…88737741672315030399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.745 Γ— 10⁹⁷(98-digit number)
57454189495904655331…77475483344630060799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.149 Γ— 10⁹⁸(99-digit number)
11490837899180931066…54950966689260121599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.298 Γ— 10⁹⁸(99-digit number)
22981675798361862132…09901933378520243199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.596 Γ— 10⁹⁸(99-digit number)
45963351596723724265…19803866757040486399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,843,177 XPMΒ·at block #6,824,886 Β· updates every 60s
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