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Block #506,254

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/22/2014, 11:33:08 PM Β· Difficulty 10.8132 Β· 6,297,807 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8e082f261ab83ff4ef73a784f50b04bab89921ad3075c4a2644f9b58a8b692fa
View on Chainz β†—

Height

#506,254

Difficulty

10.813200

Transactions

1

Size

202 B

Version

2

Bits

0ad02de0

Nonce

353,075

Timestamp

4/22/2014, 11:33:08 PM

Confirmations

6,297,807

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a7f06233d3c8181bd03b0dbdf03d7f86c69067d7c688d7bf5fd41ba779bb0ccb
Transactions (1)
Coinbasea7f06233d3c818…d41ba779bb0ccb
1 in β†’ 1 out8.5400 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.201 Γ— 10⁹⁹(100-digit number)
12016110361177869152…05970356798829476641
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
1.201 Γ— 10⁹⁹(100-digit number)
12016110361177869152…05970356798829476641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.403 Γ— 10⁹⁹(100-digit number)
24032220722355738305…11940713597658953281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.806 Γ— 10⁹⁹(100-digit number)
48064441444711476610…23881427195317906561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.612 Γ— 10⁹⁹(100-digit number)
96128882889422953221…47762854390635813121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.922 Γ— 10¹⁰⁰(101-digit number)
19225776577884590644…95525708781271626241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.845 Γ— 10¹⁰⁰(101-digit number)
38451553155769181288…91051417562543252481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.690 Γ— 10¹⁰⁰(101-digit number)
76903106311538362577…82102835125086504961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.538 Γ— 10¹⁰¹(102-digit number)
15380621262307672515…64205670250173009921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.076 Γ— 10¹⁰¹(102-digit number)
30761242524615345030…28411340500346019841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.152 Γ— 10¹⁰¹(102-digit number)
61522485049230690061…56822681000692039681
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:57,676,544 XPMΒ·at block #6,804,060 Β· updates every 60s
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