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Block #2,949,171

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/2/2018, 6:46:42 PM Β· Difficulty 11.3984 Β· 3,887,353 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
030424f9926a5d8072fd5f4b3ffb8c2f98aa95ce937f666a897e172721732500
View on Chainz β†—

Height

#2,949,171

Difficulty

11.398404

Transactions

2

Size

505 B

Version

2

Bits

0b65fdce

Nonce

1,894,675,191

Timestamp

12/2/2018, 6:46:42 PM

Confirmations

3,887,353

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

4db84041bac6b2c75b34f73d9c2cfc87abe0f0025beb0df27a77a898a0164c9a
Transactions (2)
Coinbasebd5b7ac96981ff…991ffe1db61556
1 in β†’ 1 out7.6900 XPM110 B
AbXwmGxD…4XXYP765
e19b20a6316f24…9d68285f0bf6cf
2 in β†’ 1 out8.0000 XPM305 B
ARezZb4y…FxP7ivbi
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.

7.660 Γ— 10⁹³(94-digit number)
76604557483082582136…49616832404574879559
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
7.660 Γ— 10⁹³(94-digit number)
76604557483082582136…49616832404574879559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.532 Γ— 10⁹⁴(95-digit number)
15320911496616516427…99233664809149759119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.064 Γ— 10⁹⁴(95-digit number)
30641822993233032854…98467329618299518239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.128 Γ— 10⁹⁴(95-digit number)
61283645986466065709…96934659236599036479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.225 Γ— 10⁹⁡(96-digit number)
12256729197293213141…93869318473198072959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.451 Γ— 10⁹⁡(96-digit number)
24513458394586426283…87738636946396145919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.902 Γ— 10⁹⁡(96-digit number)
49026916789172852567…75477273892792291839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.805 Γ— 10⁹⁡(96-digit number)
98053833578345705134…50954547785584583679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.961 Γ— 10⁹⁢(97-digit number)
19610766715669141026…01909095571169167359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.922 Γ— 10⁹⁢(97-digit number)
39221533431338282053…03818191142338334719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.844 Γ— 10⁹⁢(97-digit number)
78443066862676564107…07636382284676669439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,936,460 XPMΒ·at block #6,836,523 Β· updates every 60s
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