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Block #236,926

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/31/2013, 6:18:10 PM Β· Difficulty 9.9488 Β· 6,571,745 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
43c80cdadab6594dd1adaa9ba50ac8cd9e27532b938ab0ce09917b7a0cc6afb5
View on Chainz β†—

Height

#236,926

Difficulty

9.948754

Transactions

1

Size

198 B

Version

2

Bits

09f2e18d

Nonce

88,605

Timestamp

10/31/2013, 6:18:10 PM

Confirmations

6,571,745

Mined by

⛏️ P2SHAXHqpR716k7HAKyiRQyC63yPtEEXddpMfV

Merkle Root

dbc3ad3ae97306a1484841adf24f49b020246ff9d89bdc15629b14a5a0e3044e
Transactions (1)
Coinbasedbc3ad3ae97306…9b14a5a0e3044e
1 in β†’ 1 out10.0900 XPM109 B
AXHqpR71…EXddpMfV
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.

2.907 Γ— 10⁹¹(92-digit number)
29072109263217426857…12422061396438834879
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
2.907 Γ— 10⁹¹(92-digit number)
29072109263217426857…12422061396438834879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.814 Γ— 10⁹¹(92-digit number)
58144218526434853715…24844122792877669759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.162 Γ— 10⁹²(93-digit number)
11628843705286970743…49688245585755339519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.325 Γ— 10⁹²(93-digit number)
23257687410573941486…99376491171510679039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.651 Γ— 10⁹²(93-digit number)
46515374821147882972…98752982343021358079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.303 Γ— 10⁹²(93-digit number)
93030749642295765944…97505964686042716159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.860 Γ— 10⁹³(94-digit number)
18606149928459153188…95011929372085432319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.721 Γ— 10⁹³(94-digit number)
37212299856918306377…90023858744170864639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.442 Γ— 10⁹³(94-digit number)
74424599713836612755…80047717488341729279
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:57,713,413 XPMΒ·at block #6,808,670 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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