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Block #119,859

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2013, 6:11:11 PM Β· Difficulty 9.7514 Β· 6,705,433 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3504f0cca428eeb5c79eb0c32d168b909eab699910b0a587ac99f6dcfda7818a
View on Chainz β†—

Height

#119,859

Difficulty

9.751358

Transactions

1

Size

200 B

Version

2

Bits

09c05902

Nonce

87,836

Timestamp

8/16/2013, 6:11:11 PM

Confirmations

6,705,433

Mined by

⛏️ P2SHAGELmJR6aPRjt3Z8ALYc9YsGpGUuQ4Rhjr

Merkle Root

44caefe95fd05ef52c250bdf1735131f60c45aadbc9b9cb43b42dd26a27f45e1
Transactions (1)
Coinbase44caefe95fd05e…42dd26a27f45e1
1 in β†’ 1 out10.5000 XPM109 B
AGELmJR6…UuQ4Rhjr
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.

1.336 Γ— 10⁹⁸(99-digit number)
13366982793132557970…24649789724535529549
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
1.336 Γ— 10⁹⁸(99-digit number)
13366982793132557970…24649789724535529549
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.673 Γ— 10⁹⁸(99-digit number)
26733965586265115941…49299579449071059099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.346 Γ— 10⁹⁸(99-digit number)
53467931172530231882…98599158898142118199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.069 Γ— 10⁹⁹(100-digit number)
10693586234506046376…97198317796284236399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.138 Γ— 10⁹⁹(100-digit number)
21387172469012092752…94396635592568472799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.277 Γ— 10⁹⁹(100-digit number)
42774344938024185505…88793271185136945599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.554 Γ— 10⁹⁹(100-digit number)
85548689876048371011…77586542370273891199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.710 Γ— 10¹⁰⁰(101-digit number)
17109737975209674202…55173084740547782399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.421 Γ— 10¹⁰⁰(101-digit number)
34219475950419348404…10346169481095564799
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:57,846,436 XPMΒ·at block #6,825,291 Β· updates every 60s
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