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Block #2,468,104

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/11/2018, 1:52:46 PM Β· Difficulty 10.9603 Β· 4,375,545 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6232c98fbd67d23895dce6056eccce4ac77f54257e2e3275bca8f92d7bd8a9cc
View on Chainz β†—

Height

#2,468,104

Difficulty

10.960285

Transactions

1

Size

201 B

Version

2

Bits

0af5d536

Nonce

1,425,184,916

Timestamp

1/11/2018, 1:52:46 PM

Confirmations

4,375,545

Mined by

⛏️ P2SHAXFbbX6SgE9rF97hjrkhcsiKMGb3pNMSUM

Merkle Root

c2c014f7ffdb3174ec367345a6238661046e7bbd9a3b38e89a17414de1023ae6
Transactions (1)
Coinbasec2c014f7ffdb31…17414de1023ae6
1 in β†’ 1 out8.3100 XPM110 B
AXFbbX6S…b3pNMSUM
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.

3.062 Γ— 10⁹⁢(97-digit number)
30620636970923786237…49716893726956884479
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
3.062 Γ— 10⁹⁢(97-digit number)
30620636970923786237…49716893726956884479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.124 Γ— 10⁹⁢(97-digit number)
61241273941847572475…99433787453913768959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.224 Γ— 10⁹⁷(98-digit number)
12248254788369514495…98867574907827537919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.449 Γ— 10⁹⁷(98-digit number)
24496509576739028990…97735149815655075839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.899 Γ— 10⁹⁷(98-digit number)
48993019153478057980…95470299631310151679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.798 Γ— 10⁹⁷(98-digit number)
97986038306956115960…90940599262620303359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.959 Γ— 10⁹⁸(99-digit number)
19597207661391223192…81881198525240606719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.919 Γ— 10⁹⁸(99-digit number)
39194415322782446384…63762397050481213439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.838 Γ— 10⁹⁸(99-digit number)
78388830645564892768…27524794100962426879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.567 Γ— 10⁹⁹(100-digit number)
15677766129112978553…55049588201924853759
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:57,993,562 XPMΒ·at block #6,843,648 Β· updates every 60s
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