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Block #1,729,176

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/22/2016, 2:12:46 PM Β· Difficulty 10.7104 Β· 5,088,202 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9f95cc8195c44d49240b46ad9fc7143a2f85a0f8133e85f5bd30166d1fb84bbb
View on Chainz β†—

Height

#1,729,176

Difficulty

10.710379

Transactions

1

Size

243 B

Version

2

Bits

0ab5db6b

Nonce

69,465,063

Timestamp

8/22/2016, 2:12:46 PM

Confirmations

5,088,202

Mined by

⛏️ P2SHAKjaKd2Kxt1buNBYuJDadjFL1cDPsqUE8e

Merkle Root

728b43cc9ec5f5fae48e59d39988d15c562572b8ee57023d26ce76634c69ef74
Transactions (1)
Coinbase728b43cc9ec5f5…ce76634c69ef74
1 in β†’ 2 out8.7000 XPM152 B
AKjaKd2K…DPsqUE8eAXbk7f7A…Tx7JECPG
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.

5.843 Γ— 10⁹⁷(98-digit number)
58432380743433887314…84231444042515619839
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
5.843 Γ— 10⁹⁷(98-digit number)
58432380743433887314…84231444042515619839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.168 Γ— 10⁹⁸(99-digit number)
11686476148686777462…68462888085031239679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.337 Γ— 10⁹⁸(99-digit number)
23372952297373554925…36925776170062479359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.674 Γ— 10⁹⁸(99-digit number)
46745904594747109851…73851552340124958719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.349 Γ— 10⁹⁸(99-digit number)
93491809189494219703…47703104680249917439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.869 Γ— 10⁹⁹(100-digit number)
18698361837898843940…95406209360499834879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.739 Γ— 10⁹⁹(100-digit number)
37396723675797687881…90812418720999669759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.479 Γ— 10⁹⁹(100-digit number)
74793447351595375762…81624837441999339519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.495 Γ— 10¹⁰⁰(101-digit number)
14958689470319075152…63249674883998679039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.991 Γ— 10¹⁰⁰(101-digit number)
29917378940638150305…26499349767997358079
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:57,783,065 XPMΒ·at block #6,817,377 Β· updates every 60s
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