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Block #1,719,305

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2016, 4:23:44 AM Β· Difficulty 10.6706 Β· 5,076,483 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
12f9a3a09598b5c326e7f074bfb7d7cf8e416265f32fe16cb9c36b3483382716
View on Chainz β†—

Height

#1,719,305

Difficulty

10.670559

Transactions

1

Size

243 B

Version

2

Bits

0aaba9bb

Nonce

365,093,645

Timestamp

8/16/2016, 4:23:44 AM

Confirmations

5,076,483

Mined by

⛏️ P2SHAKjaKd2Kxt1buNBYuJDadjFL1cDPsqUE8e

Merkle Root

d483d997edc2674218401b8476236d22aa9ede5137efbb77530b2911ce9a29d7
Transactions (1)
Coinbased483d997edc267…0b2911ce9a29d7
1 in β†’ 2 out8.7700 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.

9.083 Γ— 10⁹⁡(96-digit number)
90832737271513054368…66776252272044771919
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
9.083 Γ— 10⁹⁡(96-digit number)
90832737271513054368…66776252272044771919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.816 Γ— 10⁹⁢(97-digit number)
18166547454302610873…33552504544089543839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.633 Γ— 10⁹⁢(97-digit number)
36333094908605221747…67105009088179087679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.266 Γ— 10⁹⁢(97-digit number)
72666189817210443494…34210018176358175359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.453 Γ— 10⁹⁷(98-digit number)
14533237963442088698…68420036352716350719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.906 Γ— 10⁹⁷(98-digit number)
29066475926884177397…36840072705432701439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.813 Γ— 10⁹⁷(98-digit number)
58132951853768354795…73680145410865402879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.162 Γ— 10⁹⁸(99-digit number)
11626590370753670959…47360290821730805759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.325 Γ— 10⁹⁸(99-digit number)
23253180741507341918…94720581643461611519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.650 Γ— 10⁹⁸(99-digit number)
46506361483014683836…89441163286923223039
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:57,610,382 XPMΒ·at block #6,795,787 Β· updates every 60s
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