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Block #164,346

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 2:56:19 PM Β· Difficulty 9.8623 Β· 6,630,703 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
419907b2860d6151a10e4e092af0af2d92bc1f656f702800b21035a7b1da0030
View on Chainz β†—

Height

#164,346

Difficulty

9.862276

Transactions

1

Size

199 B

Version

2

Bits

09dcbe20

Nonce

92,467

Timestamp

9/14/2013, 2:56:19 PM

Confirmations

6,630,703

Mined by

⛏️ P2SHAX99MLNmm1FbkFRt6WY4Zu9rUBvtidqEwE

Merkle Root

10d5114cb00ac95b75caec4aade7768122de8e1e585e7a9348052fafc9ce6c1a
Transactions (1)
Coinbase10d5114cb00ac9…052fafc9ce6c1a
1 in β†’ 1 out10.2700 XPM109 B
AX99MLNm…vtidqEwE
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.

1.199 Γ— 10⁹⁴(95-digit number)
11999871026596702181…19593827043284047119
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
1.199 Γ— 10⁹⁴(95-digit number)
11999871026596702181…19593827043284047119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.399 Γ— 10⁹⁴(95-digit number)
23999742053193404363…39187654086568094239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.799 Γ— 10⁹⁴(95-digit number)
47999484106386808726…78375308173136188479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.599 Γ— 10⁹⁴(95-digit number)
95998968212773617452…56750616346272376959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.919 Γ— 10⁹⁡(96-digit number)
19199793642554723490…13501232692544753919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.839 Γ— 10⁹⁡(96-digit number)
38399587285109446980…27002465385089507839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.679 Γ— 10⁹⁡(96-digit number)
76799174570218893961…54004930770179015679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.535 Γ— 10⁹⁢(97-digit number)
15359834914043778792…08009861540358031359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.071 Γ— 10⁹⁢(97-digit number)
30719669828087557584…16019723080716062719
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:57,604,432 XPMΒ·at block #6,795,048 Β· updates every 60s
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