Block #1,216,531

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/1/2015, 2:33:24 AM · Difficulty 10.7268 · 5,580,332 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
accc5fb8caa8b055142f258785ad8c91e801e85581648c25766fa498bf05be88

Height

#1,216,531

Difficulty

10.726754

Transactions

3

Size

947 B

Version

2

Bits

0aba0c8b

Nonce

449,277,685

Timestamp

9/1/2015, 2:33:24 AM

Confirmations

5,580,332

Merkle Root

d3b5533e5f3bde06a391b3da042b950a4612c1041db10e77d644f463bee2d47b
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.

5.275 × 10⁹⁴(95-digit number)
52750652011485056818…39841666048638530399
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
5.275 × 10⁹⁴(95-digit number)
52750652011485056818…39841666048638530399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.055 × 10⁹⁵(96-digit number)
10550130402297011363…79683332097277060799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.110 × 10⁹⁵(96-digit number)
21100260804594022727…59366664194554121599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.220 × 10⁹⁵(96-digit number)
42200521609188045454…18733328389108243199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.440 × 10⁹⁵(96-digit number)
84401043218376090909…37466656778216486399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.688 × 10⁹⁶(97-digit number)
16880208643675218181…74933313556432972799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.376 × 10⁹⁶(97-digit number)
33760417287350436363…49866627112865945599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.752 × 10⁹⁶(97-digit number)
67520834574700872727…99733254225731891199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.350 × 10⁹⁷(98-digit number)
13504166914940174545…99466508451463782399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.700 × 10⁹⁷(98-digit number)
27008333829880349090…98933016902927564799
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:57,618,918 XPM·at block #6,796,862 · updates every 60s
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