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Block #156,119

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2013, 6:17:56 PM Β· Difficulty 9.8676 Β· 6,652,893 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
840be0952ac8c529070b02062d8310ba948cc246aee808b80b99ac63061e8a59
View on Chainz β†—

Height

#156,119

Difficulty

9.867588

Transactions

1

Size

198 B

Version

2

Bits

09de1a3a

Nonce

4,352

Timestamp

9/8/2013, 6:17:56 PM

Confirmations

6,652,893

Mined by

⛏️ P2SHATr36r6GPrDWuY8aErt6RmRFsBKgmGvw5f

Merkle Root

bb6ce001d0b3214cf6dbdc9bdf1601d0b227bcc580c64507bcd3f89932c7c122
Transactions (1)
Coinbasebb6ce001d0b321…d3f89932c7c122
1 in β†’ 1 out10.2500 XPM109 B
ATr36r6G…KgmGvw5f
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.

1.862 Γ— 10⁹¹(92-digit number)
18623641846871281241…96510548071903948559
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
1.862 Γ— 10⁹¹(92-digit number)
18623641846871281241…96510548071903948559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.724 Γ— 10⁹¹(92-digit number)
37247283693742562482…93021096143807897119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.449 Γ— 10⁹¹(92-digit number)
74494567387485124965…86042192287615794239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.489 Γ— 10⁹²(93-digit number)
14898913477497024993…72084384575231588479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.979 Γ— 10⁹²(93-digit number)
29797826954994049986…44168769150463176959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.959 Γ— 10⁹²(93-digit number)
59595653909988099972…88337538300926353919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.191 Γ— 10⁹³(94-digit number)
11919130781997619994…76675076601852707839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.383 Γ— 10⁹³(94-digit number)
23838261563995239988…53350153203705415679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.767 Γ— 10⁹³(94-digit number)
47676523127990479977…06700306407410831359
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:57,716,157 XPMΒ·at block #6,809,011 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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