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Block #349,036

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/8/2014, 4:09:08 AM Β· Difficulty 10.2688 Β· 6,478,269 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
664975e1d3297182e2bc9916df70dbe9f779602434d5415df1be6c8cc0605830
View on Chainz β†—

Height

#349,036

Difficulty

10.268821

Transactions

1

Size

204 B

Version

2

Bits

0a44d16f

Nonce

192,997

Timestamp

1/8/2014, 4:09:08 AM

Confirmations

6,478,269

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

4b6203439218ea3a02390cd1d955eb397a9a9d22b56d0360e40e1ce9ad8b7886
Transactions (1)
Coinbase4b6203439218ea…0e1ce9ad8b7886
1 in β†’ 1 out9.4700 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.

2.997 Γ— 10¹⁰³(104-digit number)
29976397779012950698…53311304913973435519
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
2.997 Γ— 10¹⁰³(104-digit number)
29976397779012950698…53311304913973435519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.995 Γ— 10¹⁰³(104-digit number)
59952795558025901396…06622609827946871039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.199 Γ— 10¹⁰⁴(105-digit number)
11990559111605180279…13245219655893742079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.398 Γ— 10¹⁰⁴(105-digit number)
23981118223210360558…26490439311787484159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.796 Γ— 10¹⁰⁴(105-digit number)
47962236446420721116…52980878623574968319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.592 Γ— 10¹⁰⁴(105-digit number)
95924472892841442233…05961757247149936639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.918 Γ— 10¹⁰⁡(106-digit number)
19184894578568288446…11923514494299873279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.836 Γ— 10¹⁰⁡(106-digit number)
38369789157136576893…23847028988599746559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.673 Γ— 10¹⁰⁡(106-digit number)
76739578314273153787…47694057977199493119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.534 Γ— 10¹⁰⁢(107-digit number)
15347915662854630757…95388115954398986239
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:57,862,551 XPMΒ·at block #6,827,304 Β· updates every 60s
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