Block #196,371

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/6/2013, 10:59:21 AM · Difficulty 9.8806 · 6,628,370 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1694151855d0e3830e913644da8cf30ca48103610bd1d627d3bca29fb7bdf4e2

Height

#196,371

Difficulty

9.880620

Transactions

1

Size

4.07 KB

Version

2

Bits

09e1704a

Nonce

1,164,780,128

Timestamp

10/6/2013, 10:59:21 AM

Confirmations

6,628,370

Merkle Root

a6ffb88973104c774e4af50313469268d56bd245a22a8943272a10c1b210f560
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.

4.560 × 10⁹³(94-digit number)
45600366330300190811…99223333045068654679
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
4.560 × 10⁹³(94-digit number)
45600366330300190811…99223333045068654679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.120 × 10⁹³(94-digit number)
91200732660600381622…98446666090137309359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.824 × 10⁹⁴(95-digit number)
18240146532120076324…96893332180274618719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.648 × 10⁹⁴(95-digit number)
36480293064240152649…93786664360549237439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.296 × 10⁹⁴(95-digit number)
72960586128480305298…87573328721098474879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.459 × 10⁹⁵(96-digit number)
14592117225696061059…75146657442196949759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.918 × 10⁹⁵(96-digit number)
29184234451392122119…50293314884393899519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.836 × 10⁹⁵(96-digit number)
58368468902784244238…00586629768787799039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.167 × 10⁹⁶(97-digit number)
11673693780556848847…01173259537575598079
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:57,841,998 XPM·at block #6,824,740 · updates every 60s
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