Block #1,335,376

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/21/2015, 4:27:33 AM · Difficulty 10.8235 · 5,480,970 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
63c341569d94308360b06b460a8f3af188fe20d53b788bb04e030d0890a49e3e

Height

#1,335,376

Difficulty

10.823470

Transactions

2

Size

458 B

Version

2

Bits

0ad2cef4

Nonce

1,481,525,240

Timestamp

11/21/2015, 4:27:33 AM

Confirmations

5,480,970

Merkle Root

a98dffa76c9a0dcc8e93874468e31e719b93199b0c9ad8addacc0650a8a904d7
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.

1.263 × 10⁹⁵(96-digit number)
12632711763966845992…90086413493598509919
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
1.263 × 10⁹⁵(96-digit number)
12632711763966845992…90086413493598509919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.526 × 10⁹⁵(96-digit number)
25265423527933691984…80172826987197019839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.053 × 10⁹⁵(96-digit number)
50530847055867383968…60345653974394039679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.010 × 10⁹⁶(97-digit number)
10106169411173476793…20691307948788079359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.021 × 10⁹⁶(97-digit number)
20212338822346953587…41382615897576158719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.042 × 10⁹⁶(97-digit number)
40424677644693907175…82765231795152317439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.084 × 10⁹⁶(97-digit number)
80849355289387814350…65530463590304634879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.616 × 10⁹⁷(98-digit number)
16169871057877562870…31060927180609269759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.233 × 10⁹⁷(98-digit number)
32339742115755125740…62121854361218539519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.467 × 10⁹⁷(98-digit number)
64679484231510251480…24243708722437079039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.293 × 10⁹⁸(99-digit number)
12935896846302050296…48487417444874158079
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:57,774,892 XPM·at block #6,816,345 · updates every 60s
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