Block #936,809

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/15/2015, 12:57:50 AM · Difficulty 10.9009 · 5,873,468 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0c6ccce086fd8d6a0344594a6ffc19db627ac03774980042a4fe7de7f7ee73f5

Height

#936,809

Difficulty

10.900943

Transactions

4

Size

782 B

Version

2

Bits

0ae6a430

Nonce

959,590,538

Timestamp

2/15/2015, 12:57:50 AM

Confirmations

5,873,468

Merkle Root

198a9d34d1ba0f8d6c2b798c888509b1bc7c33893a8320215af58fd854a42a17
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.

7.435 × 10⁹⁷(98-digit number)
74356146572613194180…87724667510481879039
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
7.435 × 10⁹⁷(98-digit number)
74356146572613194180…87724667510481879039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.487 × 10⁹⁸(99-digit number)
14871229314522638836…75449335020963758079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.974 × 10⁹⁸(99-digit number)
29742458629045277672…50898670041927516159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.948 × 10⁹⁸(99-digit number)
59484917258090555344…01797340083855032319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.189 × 10⁹⁹(100-digit number)
11896983451618111068…03594680167710064639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.379 × 10⁹⁹(100-digit number)
23793966903236222137…07189360335420129279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.758 × 10⁹⁹(100-digit number)
47587933806472444275…14378720670840258559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.517 × 10⁹⁹(100-digit number)
95175867612944888551…28757441341680517119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.903 × 10¹⁰⁰(101-digit number)
19035173522588977710…57514882683361034239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.807 × 10¹⁰⁰(101-digit number)
38070347045177955420…15029765366722068479
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:57,726,289 XPM·at block #6,810,276 · updates every 60s
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