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Block #182,783

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/27/2013, 1:49:45 PM Β· Difficulty 9.8575 Β· 6,626,598 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
245335b04b5498a8f04700945bdc9d0c05b2a4968137621d669ed814ccb09114
View on Chainz β†—

Height

#182,783

Difficulty

9.857545

Transactions

1

Size

202 B

Version

2

Bits

09db8812

Nonce

72,086

Timestamp

9/27/2013, 1:49:45 PM

Confirmations

6,626,598

Mined by

⛏️ P2SHAWbQMT1UFX9Fb1nejhFo5DMbcK8Pt4ow7J

Merkle Root

7917c0e8cb14f2791676053c6e06e1ecbd67e79c104bfdb961e72382324572aa
Transactions (1)
Coinbase7917c0e8cb14f2…e72382324572aa
1 in β†’ 1 out10.2800 XPM109 B
AWbQMT1U…8Pt4ow7J
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.

2.910 Γ— 10¹⁰²(103-digit number)
29103377388410758346…65419392488645711359
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
2.910 Γ— 10¹⁰²(103-digit number)
29103377388410758346…65419392488645711359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.820 Γ— 10¹⁰²(103-digit number)
58206754776821516693…30838784977291422719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.164 Γ— 10¹⁰³(104-digit number)
11641350955364303338…61677569954582845439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.328 Γ— 10¹⁰³(104-digit number)
23282701910728606677…23355139909165690879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.656 Γ— 10¹⁰³(104-digit number)
46565403821457213354…46710279818331381759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.313 Γ— 10¹⁰³(104-digit number)
93130807642914426709…93420559636662763519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.862 Γ— 10¹⁰⁴(105-digit number)
18626161528582885341…86841119273325527039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.725 Γ— 10¹⁰⁴(105-digit number)
37252323057165770683…73682238546651054079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.450 Γ— 10¹⁰⁴(105-digit number)
74504646114331541367…47364477093302108159
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:57,719,119 XPMΒ·at block #6,809,380 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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