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Block #3,436,700

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/17/2019, 9:55:36 AM Β· Difficulty 10.9790 Β· 3,404,762 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
afc8f2b482cd78ab3fc208609314a737aa3a9fa1184e2d418908e29116ac0099
View on Chainz β†—

Height

#3,436,700

Difficulty

10.979030

Transactions

1

Size

200 B

Version

2

Bits

0afaa1be

Nonce

1,595,480,094

Timestamp

11/17/2019, 9:55:36 AM

Confirmations

3,404,762

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

8f1aac1bcfd0ef5a1c3277c8809b58af16cc9de8a70639969442a28863421db4
Transactions (1)
Coinbase8f1aac1bcfd0ef…42a28863421db4
1 in β†’ 1 out8.2800 XPM110 B
ASiq2qtK…VMhmk7yL
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.

4.665 Γ— 10⁹⁴(95-digit number)
46659401518844037917…03389026958866292881
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
4.665 Γ— 10⁹⁴(95-digit number)
46659401518844037917…03389026958866292881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.331 Γ— 10⁹⁴(95-digit number)
93318803037688075834…06778053917732585761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.866 Γ— 10⁹⁡(96-digit number)
18663760607537615166…13556107835465171521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.732 Γ— 10⁹⁡(96-digit number)
37327521215075230333…27112215670930343041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.465 Γ— 10⁹⁡(96-digit number)
74655042430150460667…54224431341860686081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.493 Γ— 10⁹⁢(97-digit number)
14931008486030092133…08448862683721372161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.986 Γ— 10⁹⁢(97-digit number)
29862016972060184267…16897725367442744321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.972 Γ— 10⁹⁢(97-digit number)
59724033944120368534…33795450734885488641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.194 Γ— 10⁹⁷(98-digit number)
11944806788824073706…67590901469770977281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.388 Γ— 10⁹⁷(98-digit number)
23889613577648147413…35181802939541954561
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,976,069 XPMΒ·at block #6,841,461 Β· updates every 60s
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