Block #925,570

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/6/2015, 10:03:48 PM · Difficulty 10.9091 · 5,917,483 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ba108efb55ec6b3066b4a80a6306809b732d0cca23376058a4bd6616bd2f2235

Height

#925,570

Difficulty

10.909063

Transactions

2

Size

1.78 KB

Version

2

Bits

0ae8b85b

Nonce

14,047,737

Timestamp

2/6/2015, 10:03:48 PM

Confirmations

5,917,483

Merkle Root

95068d4501cbb0cdd2cfeb4c342dcc890429767ff9dc227fa6118c622c1dfa5f
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.

4.441 × 10⁹⁴(95-digit number)
44418925509554567615…49756990203213701639
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
4.441 × 10⁹⁴(95-digit number)
44418925509554567615…49756990203213701639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.883 × 10⁹⁴(95-digit number)
88837851019109135231…99513980406427403279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.776 × 10⁹⁵(96-digit number)
17767570203821827046…99027960812854806559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.553 × 10⁹⁵(96-digit number)
35535140407643654092…98055921625709613119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.107 × 10⁹⁵(96-digit number)
71070280815287308184…96111843251419226239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.421 × 10⁹⁶(97-digit number)
14214056163057461636…92223686502838452479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.842 × 10⁹⁶(97-digit number)
28428112326114923273…84447373005676904959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.685 × 10⁹⁶(97-digit number)
56856224652229846547…68894746011353809919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.137 × 10⁹⁷(98-digit number)
11371244930445969309…37789492022707619839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.274 × 10⁹⁷(98-digit number)
22742489860891938619…75578984045415239679
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:57,988,782 XPM·at block #6,843,052 · updates every 60s
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