Block #606,199

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/29/2014, 2:13:32 AM · Difficulty 10.9089 · 6,218,752 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
13f621efbd0b7f9a8f4376e8ebaf770761b34a2236ad21463dc732aee19f6284

Height

#606,199

Difficulty

10.908913

Transactions

4

Size

1.28 KB

Version

2

Bits

0ae8ae83

Nonce

129,251

Timestamp

6/29/2014, 2:13:32 AM

Confirmations

6,218,752

Merkle Root

37128d00fe720879633504b0f31c96d74a3ac49e2977852e440ed61dfdeb3776
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.773 × 10⁹⁹(100-digit number)
37732713641410763863…71085644266803348799
Discovered Prime Numbers
p_k = 2^k × origin − 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 − 1
3.773 × 10⁹⁹(100-digit number)
37732713641410763863…71085644266803348799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.546 × 10⁹⁹(100-digit number)
75465427282821527727…42171288533606697599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.509 × 10¹⁰⁰(101-digit number)
15093085456564305545…84342577067213395199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.018 × 10¹⁰⁰(101-digit number)
30186170913128611090…68685154134426790399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.037 × 10¹⁰⁰(101-digit number)
60372341826257222181…37370308268853580799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.207 × 10¹⁰¹(102-digit number)
12074468365251444436…74740616537707161599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.414 × 10¹⁰¹(102-digit number)
24148936730502888872…49481233075414323199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.829 × 10¹⁰¹(102-digit number)
48297873461005777745…98962466150828646399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.659 × 10¹⁰¹(102-digit number)
96595746922011555491…97924932301657292799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.931 × 10¹⁰²(103-digit number)
19319149384402311098…95849864603314585599
Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,843,686 XPM·at block #6,824,950 · updates every 60s
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