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Block #231,835

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/28/2013, 5:42:47 PM Β· Difficulty 9.9405 Β· 6,579,229 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a5a53c3b860f70c3749503ca90bb1513504108852c140141df963963a71e8d35
View on Chainz β†—

Height

#231,835

Difficulty

9.940469

Transactions

1

Size

207 B

Version

2

Bits

09f0c29b

Nonce

83,887,079

Timestamp

10/28/2013, 5:42:47 PM

Confirmations

6,579,229

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

367a3750e50953e34b5578fc69ae86d875c004cb84eac480a6a70a98b0c89695
Transactions (1)
Coinbase367a3750e50953…a70a98b0c89695
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.161 Γ— 10⁹⁢(97-digit number)
21615405779018215156…87368298225052564479
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
2.161 Γ— 10⁹⁢(97-digit number)
21615405779018215156…87368298225052564479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.323 Γ— 10⁹⁢(97-digit number)
43230811558036430313…74736596450105128959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.646 Γ— 10⁹⁢(97-digit number)
86461623116072860627…49473192900210257919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.729 Γ— 10⁹⁷(98-digit number)
17292324623214572125…98946385800420515839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.458 Γ— 10⁹⁷(98-digit number)
34584649246429144250…97892771600841031679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.916 Γ— 10⁹⁷(98-digit number)
69169298492858288501…95785543201682063359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.383 Γ— 10⁹⁸(99-digit number)
13833859698571657700…91571086403364126719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.766 Γ— 10⁹⁸(99-digit number)
27667719397143315400…83142172806728253439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.533 Γ— 10⁹⁸(99-digit number)
55335438794286630801…66284345613456506879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.106 Γ— 10⁹⁹(100-digit number)
11067087758857326160…32568691226913013759
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:57,732,618 XPMΒ·at block #6,811,063 Β· updates every 60s
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