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Block #192,144

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/3/2013, 4:03:17 PM Β· Difficulty 9.8748 Β· 6,624,582 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1e7b2c59604c371cbbef7a319ef2682f65c7fe20cecdbe10c04ac6da7218d381
View on Chainz β†—

Height

#192,144

Difficulty

9.874836

Transactions

1

Size

205 B

Version

2

Bits

09dff53f

Nonce

3,753

Timestamp

10/3/2013, 4:03:17 PM

Confirmations

6,624,582

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

b89b63e548e088d79931c4d9983a46a2dc4b93278bf8f80783e73a65b173f0b0
Transactions (1)
Coinbaseb89b63e548e088…e73a65b173f0b0
1 in β†’ 1 out10.2400 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.

3.027 Γ— 10⁹¹(92-digit number)
30274618732047658696…19278152929852910499
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
3.027 Γ— 10⁹¹(92-digit number)
30274618732047658696…19278152929852910499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.054 Γ— 10⁹¹(92-digit number)
60549237464095317393…38556305859705820999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.210 Γ— 10⁹²(93-digit number)
12109847492819063478…77112611719411641999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.421 Γ— 10⁹²(93-digit number)
24219694985638126957…54225223438823283999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.843 Γ— 10⁹²(93-digit number)
48439389971276253915…08450446877646567999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.687 Γ— 10⁹²(93-digit number)
96878779942552507830…16900893755293135999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.937 Γ— 10⁹³(94-digit number)
19375755988510501566…33801787510586271999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.875 Γ— 10⁹³(94-digit number)
38751511977021003132…67603575021172543999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.750 Γ— 10⁹³(94-digit number)
77503023954042006264…35207150042345087999
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
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