Block #2,845,794

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/19/2018, 3:53:05 AM · Difficulty 11.7297 · 3,990,835 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2e4ba5e6626acfc7872c4605dc97a5424b59107eebd58f43ad50bc585d46081b

Height

#2,845,794

Difficulty

11.729663

Transactions

3

Size

1.33 KB

Version

2

Bits

0bbacb37

Nonce

268,185,687

Timestamp

9/19/2018, 3:53:05 AM

Confirmations

3,990,835

Merkle Root

f9ee587c03839e4872ab3b0f2c2aa627e9e8aae8be4705425c419d8dc8e37207
Transactions (3)
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.

5.641 × 10⁹⁶(97-digit number)
56417986887880442207…46285504197348300799
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
5.641 × 10⁹⁶(97-digit number)
56417986887880442207…46285504197348300799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.128 × 10⁹⁷(98-digit number)
11283597377576088441…92571008394696601599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.256 × 10⁹⁷(98-digit number)
22567194755152176883…85142016789393203199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.513 × 10⁹⁷(98-digit number)
45134389510304353766…70284033578786406399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.026 × 10⁹⁷(98-digit number)
90268779020608707532…40568067157572812799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.805 × 10⁹⁸(99-digit number)
18053755804121741506…81136134315145625599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.610 × 10⁹⁸(99-digit number)
36107511608243483012…62272268630291251199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.221 × 10⁹⁸(99-digit number)
72215023216486966025…24544537260582502399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.444 × 10⁹⁹(100-digit number)
14443004643297393205…49089074521165004799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.888 × 10⁹⁹(100-digit number)
28886009286594786410…98178149042330009599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
5.777 × 10⁹⁹(100-digit number)
57772018573189572820…96356298084660019199
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:57,937,304 XPM·at block #6,836,628 · updates every 60s
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