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Block #2,079,113

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/20/2017, 7:43:52 AM Β· Difficulty 10.8581 Β· 4,752,166 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bfd84c9dffb165b7db1268b4d30f5ec3917f6fcd9d1838eccb88700e7929ca23
View on Chainz β†—

Height

#2,079,113

Difficulty

10.858066

Transactions

1

Size

209 B

Version

2

Bits

0adbaa3a

Nonce

369,419,796

Timestamp

4/20/2017, 7:43:52 AM

Confirmations

4,752,166

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

cd02f171ea6c5ce3f295667c5b18cea42d7afe44e86ca7153b9897da458f5aa9
Transactions (1)
Coinbasecd02f171ea6c5c…9897da458f5aa9
1 in β†’ 1 out8.4700 XPM118 B
AM6GYpjw…aw86QDtR
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.

1.340 Γ— 10⁹⁸(99-digit number)
13401232521682952894…33123546380693194239
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
1.340 Γ— 10⁹⁸(99-digit number)
13401232521682952894…33123546380693194239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.680 Γ— 10⁹⁸(99-digit number)
26802465043365905788…66247092761386388479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.360 Γ— 10⁹⁸(99-digit number)
53604930086731811576…32494185522772776959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.072 Γ— 10⁹⁹(100-digit number)
10720986017346362315…64988371045545553919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.144 Γ— 10⁹⁹(100-digit number)
21441972034692724630…29976742091091107839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.288 Γ— 10⁹⁹(100-digit number)
42883944069385449261…59953484182182215679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.576 Γ— 10⁹⁹(100-digit number)
85767888138770898522…19906968364364431359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.715 Γ— 10¹⁰⁰(101-digit number)
17153577627754179704…39813936728728862719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.430 Γ— 10¹⁰⁰(101-digit number)
34307155255508359409…79627873457457725439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.861 Γ— 10¹⁰⁰(101-digit number)
68614310511016718818…59255746914915450879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,894,376 XPMΒ·at block #6,831,278 Β· updates every 60s
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