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Block #168,209

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/17/2013, 3:48:56 AM Β· Difficulty 9.8681 Β· 6,662,240 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aa619f4889a2598311225dfd7274e192b88ff6d7ad4c5f9a4d2d452deec82834
View on Chainz β†—

Height

#168,209

Difficulty

9.868090

Transactions

1

Size

202 B

Version

2

Bits

09de3b1e

Nonce

1,857

Timestamp

9/17/2013, 3:48:56 AM

Confirmations

6,662,240

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

03a4749fc1b742c39dcf642506e790c5ab5f9975104e80c6aca4f59910a53601
Transactions (1)
Coinbase03a4749fc1b742…a4f59910a53601
1 in β†’ 1 out10.2500 XPM112 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.

1.124 Γ— 10⁹⁡(96-digit number)
11243779350210564391…66694206883538211009
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
1.124 Γ— 10⁹⁡(96-digit number)
11243779350210564391…66694206883538211009
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.248 Γ— 10⁹⁡(96-digit number)
22487558700421128783…33388413767076422019
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.497 Γ— 10⁹⁡(96-digit number)
44975117400842257566…66776827534152844039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.995 Γ— 10⁹⁡(96-digit number)
89950234801684515133…33553655068305688079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.799 Γ— 10⁹⁢(97-digit number)
17990046960336903026…67107310136611376159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.598 Γ— 10⁹⁢(97-digit number)
35980093920673806053…34214620273222752319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.196 Γ— 10⁹⁢(97-digit number)
71960187841347612106…68429240546445504639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.439 Γ— 10⁹⁷(98-digit number)
14392037568269522421…36858481092891009279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.878 Γ— 10⁹⁷(98-digit number)
28784075136539044842…73716962185782018559
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:57,887,836 XPMΒ·at block #6,830,448 Β· updates every 60s
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