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Block #158,424

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2013, 8:49:23 AM Β· Difficulty 9.8675 Β· 6,648,941 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0efa8f4e38e000bd6387c513a7e30a9c410d7e744a51b1574bf50217e9d99d0b
View on Chainz β†—

Height

#158,424

Difficulty

9.867530

Transactions

2

Size

3.85 KB

Version

2

Bits

09de166e

Nonce

183,628

Timestamp

9/10/2013, 8:49:23 AM

Confirmations

6,648,941

Mined by

⛏️ P2SHARbqNWqv2Vj5LF2FcuesFtRNwxS6duczpA

Merkle Root

ada189801138ec992e991c0a156e14e367f4995b6e3cb4a063d10a718ed5af46
Transactions (2)
Coinbase53a3855e485999…257662b2a38f62
1 in β†’ 1 out10.3000 XPM109 B
ARbqNWqv…S6duczpA
abd996f2b74682…f0d2cde2dc4730
25 in β†’ 1 out50.1867 XPM3.66 KB
AS3VZynq…F8hA3vJr
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.

5.375 Γ— 10⁹²(93-digit number)
53750461174203049147…73686003459751588919
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
5.375 Γ— 10⁹²(93-digit number)
53750461174203049147…73686003459751588919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.075 Γ— 10⁹³(94-digit number)
10750092234840609829…47372006919503177839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.150 Γ— 10⁹³(94-digit number)
21500184469681219658…94744013839006355679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.300 Γ— 10⁹³(94-digit number)
43000368939362439317…89488027678012711359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.600 Γ— 10⁹³(94-digit number)
86000737878724878635…78976055356025422719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.720 Γ— 10⁹⁴(95-digit number)
17200147575744975727…57952110712050845439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.440 Γ— 10⁹⁴(95-digit number)
34400295151489951454…15904221424101690879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.880 Γ— 10⁹⁴(95-digit number)
68800590302979902908…31808442848203381759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.376 Γ— 10⁹⁡(96-digit number)
13760118060595980581…63616885696406763519
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:57,702,943 XPMΒ·at block #6,807,364 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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