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Block #3,039,411

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/5/2019, 4:27:37 AM Β· Difficulty 11.0171 Β· 3,798,597 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
faed7117691ff8b6c4277d6ca1b5b0a30b9346fcf7e1926a5997ad056ab9df77
View on Chainz β†—

Height

#3,039,411

Difficulty

11.017096

Transactions

2

Size

8.66 KB

Version

2

Bits

0b046060

Nonce

800,798,676

Timestamp

2/5/2019, 4:27:37 AM

Confirmations

3,798,597

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

fa0b58fa058a79a147eba200e0bf1e041736d54ec843ab48dfd20cbe076c596d
Transactions (2)
Coinbase4a187a8c6d671a…5427270487c24f
1 in β†’ 1 out8.3800 XPM110 B
AbXwmGxD…4XXYP765
8096d3746b89a5…2083eadd952005
58 in β†’ 2 out21823.9229 XPM8.46 KB
AeUkRdR7…C3dD541MARUqwn51…tmoj5Sey
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.

3.095 Γ— 10⁹⁡(96-digit number)
30954508468620433222…99607562801302562559
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
3.095 Γ— 10⁹⁡(96-digit number)
30954508468620433222…99607562801302562559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.190 Γ— 10⁹⁡(96-digit number)
61909016937240866445…99215125602605125119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.238 Γ— 10⁹⁢(97-digit number)
12381803387448173289…98430251205210250239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.476 Γ— 10⁹⁢(97-digit number)
24763606774896346578…96860502410420500479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.952 Γ— 10⁹⁢(97-digit number)
49527213549792693156…93721004820841000959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.905 Γ— 10⁹⁢(97-digit number)
99054427099585386312…87442009641682001919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.981 Γ— 10⁹⁷(98-digit number)
19810885419917077262…74884019283364003839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.962 Γ— 10⁹⁷(98-digit number)
39621770839834154525…49768038566728007679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.924 Γ— 10⁹⁷(98-digit number)
79243541679668309050…99536077133456015359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.584 Γ— 10⁹⁸(99-digit number)
15848708335933661810…99072154266912030719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.169 Γ— 10⁹⁸(99-digit number)
31697416671867323620…98144308533824061439
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:57,948,417 XPMΒ·at block #6,838,007 Β· updates every 60s
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