Block #201,910

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/9/2013, 9:52:03 PM · Difficulty 9.8937 · 6,590,008 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
291cc1d46bcc8c785e6658e149171590b164bf3849c5a85756cb30aec5d7be7c

Height

#201,910

Difficulty

9.893717

Transactions

1

Size

200 B

Version

2

Bits

09e4caa5

Nonce

50,810

Timestamp

10/9/2013, 9:52:03 PM

Confirmations

6,590,008

Merkle Root

d70993418e87a7dc7b949a31037e7279a4cdd643f1b068582981639942545b6c
Transactions (1)
1 in → 1 out10.2000 XPM109 B
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.

1.760 × 10⁹⁶(97-digit number)
17608924361108895778…08705391849989843141
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
1.760 × 10⁹⁶(97-digit number)
17608924361108895778…08705391849989843141
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.521 × 10⁹⁶(97-digit number)
35217848722217791556…17410783699979686281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.043 × 10⁹⁶(97-digit number)
70435697444435583113…34821567399959372561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.408 × 10⁹⁷(98-digit number)
14087139488887116622…69643134799918745121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.817 × 10⁹⁷(98-digit number)
28174278977774233245…39286269599837490241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.634 × 10⁹⁷(98-digit number)
56348557955548466490…78572539199674980481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.126 × 10⁹⁸(99-digit number)
11269711591109693298…57145078399349960961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.253 × 10⁹⁸(99-digit number)
22539423182219386596…14290156798699921921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.507 × 10⁹⁸(99-digit number)
45078846364438773192…28580313597399843841
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,579,297 XPM·at block #6,791,917 · updates every 60s
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