Block #1,595,991

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/23/2016, 1:06:05 AM · Difficulty 10.6145 · 5,230,855 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f69d5bfd60fbf41929de538af0b8cb0ffa7dc37df9e27d472f8a330dc3a728ea

Height

#1,595,991

Difficulty

10.614543

Transactions

2

Size

1.01 KB

Version

2

Bits

0a9d52b9

Nonce

762,413,823

Timestamp

5/23/2016, 1:06:05 AM

Confirmations

5,230,855

Merkle Root

5a8cdb616c7f9a5bda2239273d6edfb9e83aca4b055d765e0902261c2d1ee417
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.

2.401 × 10⁹⁵(96-digit number)
24010182352296859932…49054376424818560001
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
2.401 × 10⁹⁵(96-digit number)
24010182352296859932…49054376424818560001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.802 × 10⁹⁵(96-digit number)
48020364704593719864…98108752849637120001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.604 × 10⁹⁵(96-digit number)
96040729409187439728…96217505699274240001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.920 × 10⁹⁶(97-digit number)
19208145881837487945…92435011398548480001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.841 × 10⁹⁶(97-digit number)
38416291763674975891…84870022797096960001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.683 × 10⁹⁶(97-digit number)
76832583527349951782…69740045594193920001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.536 × 10⁹⁷(98-digit number)
15366516705469990356…39480091188387840001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.073 × 10⁹⁷(98-digit number)
30733033410939980712…78960182376775680001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.146 × 10⁹⁷(98-digit number)
61466066821879961425…57920364753551360001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.229 × 10⁹⁸(99-digit number)
12293213364375992285…15840729507102720001
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:57,858,934 XPM·at block #6,826,845 · updates every 60s
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