Block #200,606

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/9/2013, 3:03:44 AM · Difficulty 9.8898 · 6,605,462 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
653a3124704be39d965d741a0f13f7881714d794607259015a1b727d8ff1bd1c

Height

#200,606

Difficulty

9.889837

Transactions

3

Size

944 B

Version

2

Bits

09e3cc58

Nonce

60,293

Timestamp

10/9/2013, 3:03:44 AM

Confirmations

6,605,462

Merkle Root

e03b63d98d0b2fe035d0843e0af3f7b2b04b3f9b39bf2547dce7a604e5b5eee3
Transactions (3)
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.

1.310 × 10⁹³(94-digit number)
13102021679580078739…19744708564677493399
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
1.310 × 10⁹³(94-digit number)
13102021679580078739…19744708564677493399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.620 × 10⁹³(94-digit number)
26204043359160157478…39489417129354986799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.240 × 10⁹³(94-digit number)
52408086718320314956…78978834258709973599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.048 × 10⁹⁴(95-digit number)
10481617343664062991…57957668517419947199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.096 × 10⁹⁴(95-digit number)
20963234687328125982…15915337034839894399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.192 × 10⁹⁴(95-digit number)
41926469374656251965…31830674069679788799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.385 × 10⁹⁴(95-digit number)
83852938749312503930…63661348139359577599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.677 × 10⁹⁵(96-digit number)
16770587749862500786…27322696278719155199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.354 × 10⁹⁵(96-digit number)
33541175499725001572…54645392557438310399
Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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
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 × 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:57,692,623 XPM·at block #6,806,067 · updates every 60s
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