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Block #185,288

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/29/2013, 4:49:26 AM Β· Difficulty 9.8625 Β· 6,630,932 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a07f05976836222a1c365dbd8c55a55c10d72ecf83af517782134cab53f1c504
View on Chainz β†—

Height

#185,288

Difficulty

9.862527

Transactions

2

Size

1.14 KB

Version

2

Bits

09dcce91

Nonce

39,875

Timestamp

9/29/2013, 4:49:26 AM

Confirmations

6,630,932

Mined by

⛏️ P2SHANvtpRa12yh2D3uGdgT2ggcH58QjsraDJz

Merkle Root

0a3ca883fc5a45b269b011c93840c2f1825d78879f6a823250550bb69e2d1668
Transactions (2)
Coinbase36572801ac50b0…6397f2a0d180eb
1 in β†’ 1 out10.2900 XPM110 B
ANvtpRa1…QjsraDJz
1e6cd670e99e95…294a8b40a680e1
6 in β†’ 2 out31.7153 XPM965 B
AUNDVLnG…4P4xj3qDALw1LdN1…YMi8zK2e
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.

1.898 Γ— 10⁹⁡(96-digit number)
18985564992550313892…87845691036535692779
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
1.898 Γ— 10⁹⁡(96-digit number)
18985564992550313892…87845691036535692779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.797 Γ— 10⁹⁡(96-digit number)
37971129985100627784…75691382073071385559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.594 Γ— 10⁹⁡(96-digit number)
75942259970201255569…51382764146142771119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.518 Γ— 10⁹⁢(97-digit number)
15188451994040251113…02765528292285542239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.037 Γ— 10⁹⁢(97-digit number)
30376903988080502227…05531056584571084479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.075 Γ— 10⁹⁢(97-digit number)
60753807976161004455…11062113169142168959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.215 Γ— 10⁹⁷(98-digit number)
12150761595232200891…22124226338284337919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.430 Γ— 10⁹⁷(98-digit number)
24301523190464401782…44248452676568675839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.860 Γ— 10⁹⁷(98-digit number)
48603046380928803564…88496905353137351679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,773,889 XPMΒ·at block #6,816,219 Β· updates every 60s
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