Block #207,987

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/13/2013, 6:10:25 PM · Difficulty 9.9048 · 6,588,075 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9344946eb3d8c0c494051620262dcb79d3fe758581bf7f4fe322e4b05072fcca

Height

#207,987

Difficulty

9.904843

Transactions

4

Size

2.12 KB

Version

2

Bits

09e7a3c6

Nonce

85,458

Timestamp

10/13/2013, 6:10:25 PM

Confirmations

6,588,075

Merkle Root

ba664fc971ba0f2e3cc8d7b22aebf2e6a6f56981f43cfff85957352b8628bd15
Transactions (4)
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.

3.722 × 10⁹⁶(97-digit number)
37226757866823613955…49730372586787543379
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
3.722 × 10⁹⁶(97-digit number)
37226757866823613955…49730372586787543379
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.445 × 10⁹⁶(97-digit number)
74453515733647227911…99460745173575086759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.489 × 10⁹⁷(98-digit number)
14890703146729445582…98921490347150173519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.978 × 10⁹⁷(98-digit number)
29781406293458891164…97842980694300347039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.956 × 10⁹⁷(98-digit number)
59562812586917782329…95685961388600694079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.191 × 10⁹⁸(99-digit number)
11912562517383556465…91371922777201388159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.382 × 10⁹⁸(99-digit number)
23825125034767112931…82743845554402776319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.765 × 10⁹⁸(99-digit number)
47650250069534225863…65487691108805552639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.530 × 10⁹⁸(99-digit number)
95300500139068451727…30975382217611105279
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:57,612,592 XPM·at block #6,796,061 · updates every 60s
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