Block #1,201,948

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/20/2015, 5:44:11 PM · Difficulty 10.8079 · 5,613,196 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d1dce40656fc37e509ae6b44a43827c92c4dfbcc75e403c95902ef13868351c4

Height

#1,201,948

Difficulty

10.807857

Transactions

2

Size

529 B

Version

2

Bits

0acecfb4

Nonce

1,038,279,152

Timestamp

8/20/2015, 5:44:11 PM

Confirmations

5,613,196

Merkle Root

ec29f617f28efc4d723856107d8f7d63357f60f7259eaf147b478c0c4cd57320
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.

1.082 × 10⁹⁶(97-digit number)
10823937702595546512…89698773522447908481
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
1.082 × 10⁹⁶(97-digit number)
10823937702595546512…89698773522447908481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.164 × 10⁹⁶(97-digit number)
21647875405191093024…79397547044895816961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.329 × 10⁹⁶(97-digit number)
43295750810382186049…58795094089791633921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.659 × 10⁹⁶(97-digit number)
86591501620764372099…17590188179583267841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.731 × 10⁹⁷(98-digit number)
17318300324152874419…35180376359166535681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.463 × 10⁹⁷(98-digit number)
34636600648305748839…70360752718333071361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.927 × 10⁹⁷(98-digit number)
69273201296611497679…40721505436666142721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.385 × 10⁹⁸(99-digit number)
13854640259322299535…81443010873332285441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.770 × 10⁹⁸(99-digit number)
27709280518644599071…62886021746664570881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.541 × 10⁹⁸(99-digit number)
55418561037289198143…25772043493329141761
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,765,246 XPM·at block #6,815,143 · updates every 60s
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