Block #1,608,159

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/31/2016, 1:08:14 PM · Difficulty 10.6095 · 5,233,618 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb85e6155a031a24bda295cea0e4dd3a163b5d68325bc2097a104e4e74dff3ec

Height

#1,608,159

Difficulty

10.609451

Transactions

2

Size

1.38 KB

Version

2

Bits

0a9c04f3

Nonce

659,675,946

Timestamp

5/31/2016, 1:08:14 PM

Confirmations

5,233,618

Merkle Root

c1d46bd649c381f433077a691edcedd4d6c41f3f7a94229493744badcabda925
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.

6.410 × 10⁹⁵(96-digit number)
64107504699609523340…23242757338231879681
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
6.410 × 10⁹⁵(96-digit number)
64107504699609523340…23242757338231879681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.282 × 10⁹⁶(97-digit number)
12821500939921904668…46485514676463759361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.564 × 10⁹⁶(97-digit number)
25643001879843809336…92971029352927518721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.128 × 10⁹⁶(97-digit number)
51286003759687618672…85942058705855037441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.025 × 10⁹⁷(98-digit number)
10257200751937523734…71884117411710074881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.051 × 10⁹⁷(98-digit number)
20514401503875047468…43768234823420149761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.102 × 10⁹⁷(98-digit number)
41028803007750094937…87536469646840299521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.205 × 10⁹⁷(98-digit number)
82057606015500189875…75072939293680599041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.641 × 10⁹⁸(99-digit number)
16411521203100037975…50145878587361198081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.282 × 10⁹⁸(99-digit number)
32823042406200075950…00291757174722396161
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:57,978,592 XPM·at block #6,841,776 · updates every 60s
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