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Block #1,794,606

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/6/2016, 4:42:50 AM Β· Difficulty 10.7736 Β· 5,032,193 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
40f83044b03536d876d7739696c13892c748b5fa127d0da70917777adf4d89a9
View on Chainz β†—

Height

#1,794,606

Difficulty

10.773574

Transactions

1

Size

242 B

Version

2

Bits

0ac608f6

Nonce

180,369,035

Timestamp

10/6/2016, 4:42:50 AM

Confirmations

5,032,193

Mined by

⛏️ P2SHATd5Bq5SNppozp9HDzLQKxc4KVPcfPgHVj

Merkle Root

b6358efc79cca695fb1909bc3729f563de82471ed3955a10e728017e19d1a973
Transactions (1)
Coinbaseb6358efc79cca6…28017e19d1a973
1 in β†’ 2 out8.6000 XPM152 B
ATd5Bq5S…PcfPgHVjALPu3s2c…EJXLjVFh
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.

5.478 Γ— 10⁹⁴(95-digit number)
54780201020373187635…90984889945340373759
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
5.478 Γ— 10⁹⁴(95-digit number)
54780201020373187635…90984889945340373759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.095 Γ— 10⁹⁡(96-digit number)
10956040204074637527…81969779890680747519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.191 Γ— 10⁹⁡(96-digit number)
21912080408149275054…63939559781361495039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.382 Γ— 10⁹⁡(96-digit number)
43824160816298550108…27879119562722990079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.764 Γ— 10⁹⁡(96-digit number)
87648321632597100216…55758239125445980159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.752 Γ— 10⁹⁢(97-digit number)
17529664326519420043…11516478250891960319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.505 Γ— 10⁹⁢(97-digit number)
35059328653038840086…23032956501783920639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.011 Γ— 10⁹⁢(97-digit number)
70118657306077680172…46065913003567841279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.402 Γ— 10⁹⁷(98-digit number)
14023731461215536034…92131826007135682559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.804 Γ— 10⁹⁷(98-digit number)
28047462922431072069…84263652014271365119
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:57,858,555 XPMΒ·at block #6,826,798 Β· updates every 60s
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