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Block #2,348,164

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/23/2017, 11:12:21 AM Β· Difficulty 10.8969 Β· 4,493,944 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
39584f97ad5dcdb16b80330d8e01886a3547fc665c35ba2ca4b55f03b26c5dcf
View on Chainz β†—

Height

#2,348,164

Difficulty

10.896930

Transactions

1

Size

199 B

Version

2

Bits

0ae59d2d

Nonce

344,363,236

Timestamp

10/23/2017, 11:12:21 AM

Confirmations

4,493,944

Mined by

⛏️ P2SHAHtm9K46Y2KPWUNZtk2UeKECT3Q4tk5YeR

Merkle Root

e2a4a413168bd5bb893a2c38b630e23d68644908ac9dfb84d4a4395ae1213a8e
Transactions (1)
Coinbasee2a4a413168bd5…a4395ae1213a8e
1 in β†’ 1 out8.4100 XPM109 B
AHtm9K46…Q4tk5YeR
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.

6.158 Γ— 10⁹⁡(96-digit number)
61582462076987374535…80487892086469032959
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
6.158 Γ— 10⁹⁡(96-digit number)
61582462076987374535…80487892086469032959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.231 Γ— 10⁹⁢(97-digit number)
12316492415397474907…60975784172938065919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.463 Γ— 10⁹⁢(97-digit number)
24632984830794949814…21951568345876131839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.926 Γ— 10⁹⁢(97-digit number)
49265969661589899628…43903136691752263679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.853 Γ— 10⁹⁢(97-digit number)
98531939323179799256…87806273383504527359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.970 Γ— 10⁹⁷(98-digit number)
19706387864635959851…75612546767009054719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.941 Γ— 10⁹⁷(98-digit number)
39412775729271919702…51225093534018109439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.882 Γ— 10⁹⁷(98-digit number)
78825551458543839404…02450187068036218879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.576 Γ— 10⁹⁸(99-digit number)
15765110291708767880…04900374136072437759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.153 Γ— 10⁹⁸(99-digit number)
31530220583417535761…09800748272144875519
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:57,981,251 XPMΒ·at block #6,842,107 Β· updates every 60s
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