Block #602,684

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/26/2014, 11:35:38 AM · Difficulty 10.9130 · 6,206,728 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9c64a5e28a36875efbd806936cc487bd10737710a42bd5d19ea51de11a29fa98

Height

#602,684

Difficulty

10.913049

Transactions

1

Size

663 B

Version

2

Bits

0ae9bd97

Nonce

350,615

Timestamp

6/26/2014, 11:35:38 AM

Confirmations

6,206,728

Merkle Root

5a8755f8989192391b3f46526cf6fa11912220fc312f3a561bc2ffc58734efdd
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.

1.618 × 10⁹⁵(96-digit number)
16189621670750931323…60480634439767925759
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
1.618 × 10⁹⁵(96-digit number)
16189621670750931323…60480634439767925759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.237 × 10⁹⁵(96-digit number)
32379243341501862647…20961268879535851519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.475 × 10⁹⁵(96-digit number)
64758486683003725294…41922537759071703039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.295 × 10⁹⁶(97-digit number)
12951697336600745058…83845075518143406079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.590 × 10⁹⁶(97-digit number)
25903394673201490117…67690151036286812159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.180 × 10⁹⁶(97-digit number)
51806789346402980235…35380302072573624319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.036 × 10⁹⁷(98-digit number)
10361357869280596047…70760604145147248639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.072 × 10⁹⁷(98-digit number)
20722715738561192094…41521208290294497279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.144 × 10⁹⁷(98-digit number)
41445431477122384188…83042416580588994559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.289 × 10⁹⁷(98-digit number)
82890862954244768376…66084833161177989119
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:57,719,371 XPM·at block #6,809,411 · updates every 60s
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