Block #1,186,961

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/8/2015, 4:12:03 PM · Difficulty 10.8799 · 5,629,432 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
68debe164b2a8e98d87a524a7b0f3c8858be3782158ded2db3a96a9df75c6837

Height

#1,186,961

Difficulty

10.879894

Transactions

4

Size

1.59 KB

Version

2

Bits

0ae140bb

Nonce

1,726,805,950

Timestamp

8/8/2015, 4:12:03 PM

Confirmations

5,629,432

Merkle Root

1e7134526f006163d50cecb87bb66d39db88061584b8cf382eb98741e75f78cd
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.

9.623 × 10⁹⁶(97-digit number)
96238520265919204074…18499137398486520319
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
9.623 × 10⁹⁶(97-digit number)
96238520265919204074…18499137398486520319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.924 × 10⁹⁷(98-digit number)
19247704053183840814…36998274796973040639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.849 × 10⁹⁷(98-digit number)
38495408106367681629…73996549593946081279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.699 × 10⁹⁷(98-digit number)
76990816212735363259…47993099187892162559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.539 × 10⁹⁸(99-digit number)
15398163242547072651…95986198375784325119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.079 × 10⁹⁸(99-digit number)
30796326485094145303…91972396751568650239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.159 × 10⁹⁸(99-digit number)
61592652970188290607…83944793503137300479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.231 × 10⁹⁹(100-digit number)
12318530594037658121…67889587006274600959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.463 × 10⁹⁹(100-digit number)
24637061188075316243…35779174012549201919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.927 × 10⁹⁹(100-digit number)
49274122376150632486…71558348025098403839
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,775,267 XPM·at block #6,816,392 · updates every 60s
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