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Block #3,030,469

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/29/2019, 3:10:44 PM Β· Difficulty 11.1086 Β· 3,811,607 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b0677ea7b71c5285f9051e91b9bbdbb7a1969a6a328af380d16011d53a4eae2b
View on Chainz β†—

Height

#3,030,469

Difficulty

11.108634

Transactions

2

Size

24.01 KB

Version

2

Bits

0b1bcf6d

Nonce

130,054,982

Timestamp

1/29/2019, 3:10:44 PM

Confirmations

3,811,607

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

2eeb7e0c2bac22b141d5de6b9e36de4cf4304c555b265ed1442db8d5fbc6b8b5
Transactions (2)
Coinbased5bc50ab2951af…0817b6c3d025a6
1 in β†’ 1 out8.3400 XPM110 B
AbXwmGxD…4XXYP765
6ebe400038b15e…98d334cc3cc400
165 in β†’ 1 out332.8124 XPM23.81 KB
AWWtytp9…KRDQvtU2
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.

2.910 Γ— 10⁹⁴(95-digit number)
29102027914916628577…49535936710529227679
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
2.910 Γ— 10⁹⁴(95-digit number)
29102027914916628577…49535936710529227679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.820 Γ— 10⁹⁴(95-digit number)
58204055829833257154…99071873421058455359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.164 Γ— 10⁹⁡(96-digit number)
11640811165966651430…98143746842116910719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.328 Γ— 10⁹⁡(96-digit number)
23281622331933302861…96287493684233821439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.656 Γ— 10⁹⁡(96-digit number)
46563244663866605723…92574987368467642879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.312 Γ— 10⁹⁡(96-digit number)
93126489327733211447…85149974736935285759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.862 Γ— 10⁹⁢(97-digit number)
18625297865546642289…70299949473870571519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.725 Γ— 10⁹⁢(97-digit number)
37250595731093284578…40599898947741143039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.450 Γ— 10⁹⁢(97-digit number)
74501191462186569157…81199797895482286079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.490 Γ— 10⁹⁷(98-digit number)
14900238292437313831…62399595790964572159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.980 Γ— 10⁹⁷(98-digit number)
29800476584874627663…24799191581929144319
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:57,980,993 XPMΒ·at block #6,842,075 Β· updates every 60s
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