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Block #184,858

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/28/2013, 10:15:42 PM Β· Difficulty 9.8614 Β· 6,620,286 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
afac3f6d4d1b31f27ed7ef9819ae6b5e124a0ca5f76ff279b2f36cffad679724
View on Chainz β†—

Height

#184,858

Difficulty

9.861403

Transactions

2

Size

573 B

Version

2

Bits

09dc84ec

Nonce

312,661

Timestamp

9/28/2013, 10:15:42 PM

Confirmations

6,620,286

Mined by

⛏️ P2SHAFvfCa1WUvxPh1KkHgJxPR6DVF3pZgbFWa

Merkle Root

9ef4d11f43cbda64c42fdb400a75a1ef2d5fdaef85b5caa63652cf5b8329522e
Transactions (2)
Coinbase4188842bd6ad59…c4ae47cee50fde
1 in β†’ 1 out10.2800 XPM110 B
AFvfCa1W…3pZgbFWa
7a6372f046aa7a…1669a218261ebb
2 in β†’ 2 out250.0150 XPM374 B
AFqDj4vn…D3w8GBCwANbegevv…AwXn311D
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.

1.501 Γ— 10⁹³(94-digit number)
15017802651498531505…63232859086664311159
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
1.501 Γ— 10⁹³(94-digit number)
15017802651498531505…63232859086664311159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.003 Γ— 10⁹³(94-digit number)
30035605302997063011…26465718173328622319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.007 Γ— 10⁹³(94-digit number)
60071210605994126022…52931436346657244639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.201 Γ— 10⁹⁴(95-digit number)
12014242121198825204…05862872693314489279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.402 Γ— 10⁹⁴(95-digit number)
24028484242397650408…11725745386628978559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.805 Γ— 10⁹⁴(95-digit number)
48056968484795300817…23451490773257957119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.611 Γ— 10⁹⁴(95-digit number)
96113936969590601635…46902981546515914239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.922 Γ— 10⁹⁡(96-digit number)
19222787393918120327…93805963093031828479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.844 Γ— 10⁹⁡(96-digit number)
38445574787836240654…87611926186063656959
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:57,685,217 XPMΒ·at block #6,805,143 Β· updates every 60s
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