Block #1,341,116

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/25/2015, 1:34:12 PM · Difficulty 10.8027 · 5,502,107 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c35315869312d69b7f4f0fe551c2153c2fc625c4d49db900ecf4c82310183ace

Height

#1,341,116

Difficulty

10.802660

Transactions

3

Size

1.76 KB

Version

2

Bits

0acd7b20

Nonce

1,243,557,143

Timestamp

11/25/2015, 1:34:12 PM

Confirmations

5,502,107

Merkle Root

a3bf3f5a65cc733500887037367da67cc572ec9c9b5311f140470d26d6a3ae73
Transactions (3)
1 in → 1 out8.5900 XPM110 B
3 in → 1 out11.9900 XPM489 B
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.

2.827 × 10⁹⁴(95-digit number)
28270158980517116708…62898827020402898719
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
2.827 × 10⁹⁴(95-digit number)
28270158980517116708…62898827020402898719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.654 × 10⁹⁴(95-digit number)
56540317961034233416…25797654040805797439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.130 × 10⁹⁵(96-digit number)
11308063592206846683…51595308081611594879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.261 × 10⁹⁵(96-digit number)
22616127184413693366…03190616163223189759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.523 × 10⁹⁵(96-digit number)
45232254368827386733…06381232326446379519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.046 × 10⁹⁵(96-digit number)
90464508737654773467…12762464652892759039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.809 × 10⁹⁶(97-digit number)
18092901747530954693…25524929305785518079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.618 × 10⁹⁶(97-digit number)
36185803495061909386…51049858611571036159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.237 × 10⁹⁶(97-digit number)
72371606990123818773…02099717223142072319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.447 × 10⁹⁷(98-digit number)
14474321398024763754…04199434446284144639
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:57,990,158 XPM·at block #6,843,222 · updates every 60s
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