Block #1,338,383

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/23/2015, 8:02:10 PM · Difficulty 10.7929 · 5,473,493 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
90355b34415aef6753973bae0caaa786b9a9a53a14ff999c555838d90a411e8c

Height

#1,338,383

Difficulty

10.792936

Transactions

2

Size

1.11 KB

Version

2

Bits

0acafddf

Nonce

49,748,929

Timestamp

11/23/2015, 8:02:10 PM

Confirmations

5,473,493

Merkle Root

568f76e8002e58f9f99df6ef8fdb4f4491ea49b85ebdbaba32fe690fb0c41267
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.

1.215 × 10⁹⁴(95-digit number)
12150236825377050411…47087224578822209079
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
1.215 × 10⁹⁴(95-digit number)
12150236825377050411…47087224578822209079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.430 × 10⁹⁴(95-digit number)
24300473650754100822…94174449157644418159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.860 × 10⁹⁴(95-digit number)
48600947301508201645…88348898315288836319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.720 × 10⁹⁴(95-digit number)
97201894603016403290…76697796630577672639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.944 × 10⁹⁵(96-digit number)
19440378920603280658…53395593261155345279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.888 × 10⁹⁵(96-digit number)
38880757841206561316…06791186522310690559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.776 × 10⁹⁵(96-digit number)
77761515682413122632…13582373044621381119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.555 × 10⁹⁶(97-digit number)
15552303136482624526…27164746089242762239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.110 × 10⁹⁶(97-digit number)
31104606272965249052…54329492178485524479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.220 × 10⁹⁶(97-digit number)
62209212545930498105…08658984356971048959
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:57,739,101 XPM·at block #6,811,875 · updates every 60s
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