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Block #1,864,994

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/25/2016, 2:47:35 AM Β· Difficulty 10.6992 Β· 4,967,580 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fcfa36c873dbaf6ada6ca5ca6d044a8b1cd13d7cf4a50b5519b91ef6baa9e501
View on Chainz β†—

Height

#1,864,994

Difficulty

10.699164

Transactions

1

Size

243 B

Version

2

Bits

0ab2fc63

Nonce

12,963,087

Timestamp

11/25/2016, 2:47:35 AM

Confirmations

4,967,580

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

05d7bd2fd81edd827270430ce850ac3fc9add84426b7a78d163af9f3ce4124af
Transactions (1)
Coinbase05d7bd2fd81edd…3af9f3ce4124af
1 in β†’ 2 out8.7200 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…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.

1.975 Γ— 10⁹⁢(97-digit number)
19759126483699628613…13748307130888519679
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
1.975 Γ— 10⁹⁢(97-digit number)
19759126483699628613…13748307130888519679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.951 Γ— 10⁹⁢(97-digit number)
39518252967399257226…27496614261777039359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.903 Γ— 10⁹⁢(97-digit number)
79036505934798514452…54993228523554078719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.580 Γ— 10⁹⁷(98-digit number)
15807301186959702890…09986457047108157439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.161 Γ— 10⁹⁷(98-digit number)
31614602373919405780…19972914094216314879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.322 Γ— 10⁹⁷(98-digit number)
63229204747838811561…39945828188432629759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.264 Γ— 10⁹⁸(99-digit number)
12645840949567762312…79891656376865259519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.529 Γ— 10⁹⁸(99-digit number)
25291681899135524624…59783312753730519039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.058 Γ— 10⁹⁸(99-digit number)
50583363798271049249…19566625507461038079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.011 Γ— 10⁹⁹(100-digit number)
10116672759654209849…39133251014922076159
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:57,904,752 XPMΒ·at block #6,832,573 Β· updates every 60s
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