Block #1,171,080

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 7/26/2015, 9:14:08 AM · Difficulty 10.9366 · 5,668,298 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fd28d2d2bac439c7babeae47bb3730c3dc3bb6852c9774b7de527a113f2d1c4d

Height

#1,171,080

Difficulty

10.936641

Transactions

2

Size

1.28 KB

Version

2

Bits

0aefc7ac

Nonce

58,329,974

Timestamp

7/26/2015, 9:14:08 AM

Confirmations

5,668,298

Merkle Root

97cbe40db7879cb48c5675078a139a4262bd4706b5bd8051df0a42fbbdc5d59d
Transactions (2)
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.

2.036 × 10⁹⁴(95-digit number)
20368802573567125092…03171519062030635299
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
2.036 × 10⁹⁴(95-digit number)
20368802573567125092…03171519062030635299
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.073 × 10⁹⁴(95-digit number)
40737605147134250185…06343038124061270599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.147 × 10⁹⁴(95-digit number)
81475210294268500370…12686076248122541199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.629 × 10⁹⁵(96-digit number)
16295042058853700074…25372152496245082399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.259 × 10⁹⁵(96-digit number)
32590084117707400148…50744304992490164799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.518 × 10⁹⁵(96-digit number)
65180168235414800296…01488609984980329599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.303 × 10⁹⁶(97-digit number)
13036033647082960059…02977219969960659199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.607 × 10⁹⁶(97-digit number)
26072067294165920118…05954439939921318399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.214 × 10⁹⁶(97-digit number)
52144134588331840237…11908879879842636799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.042 × 10⁹⁷(98-digit number)
10428826917666368047…23817759759685273599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.085 × 10⁹⁷(98-digit number)
20857653835332736094…47635519519370547199
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,959,307 XPM·at block #6,839,377 · updates every 60s
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