Block #1,438,532

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/1/2016, 2:04:34 PM · Difficulty 10.7848 · 5,394,494 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ea26cf0d3d8893e6c8d98067248eceb75bed2e5d27d93ca89381ab997bbad0e

Height

#1,438,532

Difficulty

10.784845

Transactions

3

Size

2.53 KB

Version

2

Bits

0ac8eba2

Nonce

964,121,524

Timestamp

2/1/2016, 2:04:34 PM

Confirmations

5,394,494

Merkle Root

a6e015d6b59b45191e3068b03c14c64c854eaad02f7a130c18309ce580ba6d4f
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.

5.396 × 10⁹⁴(95-digit number)
53965220462795696333…37341630526085626121
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
5.396 × 10⁹⁴(95-digit number)
53965220462795696333…37341630526085626121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.079 × 10⁹⁵(96-digit number)
10793044092559139266…74683261052171252241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.158 × 10⁹⁵(96-digit number)
21586088185118278533…49366522104342504481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.317 × 10⁹⁵(96-digit number)
43172176370236557066…98733044208685008961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.634 × 10⁹⁵(96-digit number)
86344352740473114133…97466088417370017921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.726 × 10⁹⁶(97-digit number)
17268870548094622826…94932176834740035841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.453 × 10⁹⁶(97-digit number)
34537741096189245653…89864353669480071681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.907 × 10⁹⁶(97-digit number)
69075482192378491306…79728707338960143361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.381 × 10⁹⁷(98-digit number)
13815096438475698261…59457414677920286721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.763 × 10⁹⁷(98-digit number)
27630192876951396522…18914829355840573441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.526 × 10⁹⁷(98-digit number)
55260385753902793045…37829658711681146881
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,908,384 XPM·at block #6,833,025 · updates every 60s
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