Block #208,654

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/14/2013, 3:20:17 AM · Difficulty 9.9071 · 6,600,567 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4b1e01ff85c5734ee7701b072dabe8acfdcafdc1b2b17d5390a6422cf45f1777

Height

#208,654

Difficulty

9.907059

Transactions

2

Size

1.25 KB

Version

2

Bits

09e8350c

Nonce

23,158

Timestamp

10/14/2013, 3:20:17 AM

Confirmations

6,600,567

Merkle Root

8279441c9f914adaebb77596cad420c38f62d38e30cd103371a1e0d8240ff138
Transactions (2)
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.

1.773 × 10⁹⁶(97-digit number)
17733475051701762274…18602991731131102719
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
1.773 × 10⁹⁶(97-digit number)
17733475051701762274…18602991731131102719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.546 × 10⁹⁶(97-digit number)
35466950103403524548…37205983462262205439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.093 × 10⁹⁶(97-digit number)
70933900206807049097…74411966924524410879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.418 × 10⁹⁷(98-digit number)
14186780041361409819…48823933849048821759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.837 × 10⁹⁷(98-digit number)
28373560082722819639…97647867698097643519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.674 × 10⁹⁷(98-digit number)
56747120165445639278…95295735396195287039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.134 × 10⁹⁸(99-digit number)
11349424033089127855…90591470792390574079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.269 × 10⁹⁸(99-digit number)
22698848066178255711…81182941584781148159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.539 × 10⁹⁸(99-digit number)
45397696132356511422…62365883169562296319
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:57,717,830 XPM·at block #6,809,220 · updates every 60s
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