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Block #789,991

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/30/2014, 10:29:01 PM Β· Difficulty 10.9740 Β· 6,024,234 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f48b3484778db796d6889bda5ec885c296d8f6f405555f3292a6b372feb7128e
View on Chainz β†—

Height

#789,991

Difficulty

10.973998

Transactions

1

Size

242 B

Version

2

Bits

0af957ef

Nonce

184,060,532

Timestamp

10/30/2014, 10:29:01 PM

Confirmations

6,024,234

Mined by

⛏️ P2SHAYFivgcJEqUfH1zEbfNs35USz3FT8wELGF

Merkle Root

ae534db0bb22eb17136ea65867c4e7c2955137221a90708b8428d62fa17ab748
Transactions (1)
Coinbaseae534db0bb22eb…28d62fa17ab748
1 in β†’ 2 out8.2900 XPM152 B
AYFivgcJ…FT8wELGFALPu3s2c…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.

6.483 Γ— 10⁹⁡(96-digit number)
64834373745550285557…31913245369703766999
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
6.483 Γ— 10⁹⁡(96-digit number)
64834373745550285557…31913245369703766999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.296 Γ— 10⁹⁢(97-digit number)
12966874749110057111…63826490739407533999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.593 Γ— 10⁹⁢(97-digit number)
25933749498220114223…27652981478815067999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.186 Γ— 10⁹⁢(97-digit number)
51867498996440228446…55305962957630135999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.037 Γ— 10⁹⁷(98-digit number)
10373499799288045689…10611925915260271999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.074 Γ— 10⁹⁷(98-digit number)
20746999598576091378…21223851830520543999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.149 Γ— 10⁹⁷(98-digit number)
41493999197152182757…42447703661041087999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.298 Γ— 10⁹⁷(98-digit number)
82987998394304365514…84895407322082175999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.659 Γ— 10⁹⁸(99-digit number)
16597599678860873102…69790814644164351999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.319 Γ— 10⁹⁸(99-digit number)
33195199357721746205…39581629288328703999
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:57,757,870 XPMΒ·at block #6,814,224 Β· updates every 60s
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