Block #1,270,965

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/7/2015, 1:09:04 PM · Difficulty 10.8163 · 5,538,407 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f5fb8eb7e450fc1c41a1c83b2650c66d8c8053910c1f2aac2f532ffb80d0e205

Height

#1,270,965

Difficulty

10.816284

Transactions

2

Size

1.18 KB

Version

2

Bits

0ad0f7fd

Nonce

494,323,500

Timestamp

10/7/2015, 1:09:04 PM

Confirmations

5,538,407

Merkle Root

38be2d0a06eca2c90b18499bedae648fe77ace038f157bedeeb2b54f838f20c9
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.

4.253 × 10⁹⁵(96-digit number)
42535444825970104204…75150099881921368961
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
4.253 × 10⁹⁵(96-digit number)
42535444825970104204…75150099881921368961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.507 × 10⁹⁵(96-digit number)
85070889651940208408…50300199763842737921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.701 × 10⁹⁶(97-digit number)
17014177930388041681…00600399527685475841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.402 × 10⁹⁶(97-digit number)
34028355860776083363…01200799055370951681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.805 × 10⁹⁶(97-digit number)
68056711721552166726…02401598110741903361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.361 × 10⁹⁷(98-digit number)
13611342344310433345…04803196221483806721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.722 × 10⁹⁷(98-digit number)
27222684688620866690…09606392442967613441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.444 × 10⁹⁷(98-digit number)
54445369377241733381…19212784885935226881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.088 × 10⁹⁸(99-digit number)
10889073875448346676…38425569771870453761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.177 × 10⁹⁸(99-digit number)
21778147750896693352…76851139543740907521
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,719,045 XPM·at block #6,809,371 · updates every 60s
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