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Block #2,991,221

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/1/2019, 5:15:18 PM Β· Difficulty 11.2601 Β· 3,851,002 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
68e763269edc39b4bdf4e1b0ab7a65335acad379e9368b593b9682b404e106d3
View on Chainz β†—

Height

#2,991,221

Difficulty

11.260055

Transactions

2

Size

869 B

Version

2

Bits

0b4292fc

Nonce

365,326,124

Timestamp

1/1/2019, 5:15:18 PM

Confirmations

3,851,002

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

ab1eb0e92b4a918e40af67dbe262931b73a4f664b132f600f754ddbd67fe2adb
Transactions (2)
Coinbase0972d1bca99640…d5b12c83691e98
1 in β†’ 1 out7.8800 XPM110 B
AUhjokok…k5m93PZR
a217a9511a4b98…f69daba2d79283
4 in β†’ 2 out600.0100 XPM669 B
AbadyHGq…syxq2CpkAKVuW4y2…cWJ2ESUC
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.

4.087 Γ— 10⁹⁴(95-digit number)
40874795144169249449…13192938002077424969
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
4.087 Γ— 10⁹⁴(95-digit number)
40874795144169249449…13192938002077424969
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.174 Γ— 10⁹⁴(95-digit number)
81749590288338498899…26385876004154849939
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.634 Γ— 10⁹⁡(96-digit number)
16349918057667699779…52771752008309699879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.269 Γ— 10⁹⁡(96-digit number)
32699836115335399559…05543504016619399759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.539 Γ— 10⁹⁡(96-digit number)
65399672230670799119…11087008033238799519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.307 Γ— 10⁹⁢(97-digit number)
13079934446134159823…22174016066477599039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.615 Γ— 10⁹⁢(97-digit number)
26159868892268319647…44348032132955198079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.231 Γ— 10⁹⁢(97-digit number)
52319737784536639295…88696064265910396159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.046 Γ— 10⁹⁷(98-digit number)
10463947556907327859…77392128531820792319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.092 Γ— 10⁹⁷(98-digit number)
20927895113814655718…54784257063641584639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.185 Γ— 10⁹⁷(98-digit number)
41855790227629311436…09568514127283169279
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:57,982,182 XPMΒ·at block #6,842,222 Β· updates every 60s
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