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Block #158,004

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2013, 1:10:43 AM Β· Difficulty 9.8685 Β· 6,639,848 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c90e99355f2c5e89002dbd9a62af4bca77b4d72befb8b9bb59e41708409b2c52
View on Chainz β†—

Height

#158,004

Difficulty

9.868495

Transactions

1

Size

197 B

Version

2

Bits

09de55b6

Nonce

76,563

Timestamp

9/10/2013, 1:10:43 AM

Confirmations

6,639,848

Mined by

⛏️ P2SHAKhaGKFX4s17sd56QzVFtsa8mSKjeAXtBv

Merkle Root

822f47a96bd119c160e0eb1cad5b7232c3955586302ca08d83553c3741e3bab4
Transactions (1)
Coinbase822f47a96bd119…553c3741e3bab4
1 in β†’ 1 out10.2500 XPM109 B
AKhaGKFX…KjeAXtBv
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.

2.445 Γ— 10⁹⁰(91-digit number)
24458662818676717291…14780557794729159999
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
2.445 Γ— 10⁹⁰(91-digit number)
24458662818676717291…14780557794729159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.891 Γ— 10⁹⁰(91-digit number)
48917325637353434583…29561115589458319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.783 Γ— 10⁹⁰(91-digit number)
97834651274706869166…59122231178916639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.956 Γ— 10⁹¹(92-digit number)
19566930254941373833…18244462357833279999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.913 Γ— 10⁹¹(92-digit number)
39133860509882747666…36488924715666559999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.826 Γ— 10⁹¹(92-digit number)
78267721019765495332…72977849431333119999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.565 Γ— 10⁹²(93-digit number)
15653544203953099066…45955698862666239999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.130 Γ— 10⁹²(93-digit number)
31307088407906198133…91911397725332479999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.261 Γ— 10⁹²(93-digit number)
62614176815812396266…83822795450664959999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.252 Γ— 10⁹³(94-digit number)
12522835363162479253…67645590901329919999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,626,800 XPMΒ·at block #6,797,851 Β· updates every 60s
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