Block #950,917

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/24/2015, 11:05:03 PM · Difficulty 10.8981 · 5,875,799 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
91ea3e986eabf87d04dbc7dd8ce073f734bee5d41cc80557aab29b6eda8f0177

Height

#950,917

Difficulty

10.898143

Transactions

4

Size

1.73 KB

Version

2

Bits

0ae5ecba

Nonce

1,097,284,657

Timestamp

2/24/2015, 11:05:03 PM

Confirmations

5,875,799

Merkle Root

0edcc7223eaa460637d9b20b2f3687f3e8afaffd1ae0619fefd4269cecffdbf9
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.

7.924 × 10⁹⁶(97-digit number)
79243636091736876833…90558248946523025601
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
7.924 × 10⁹⁶(97-digit number)
79243636091736876833…90558248946523025601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.584 × 10⁹⁷(98-digit number)
15848727218347375366…81116497893046051201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.169 × 10⁹⁷(98-digit number)
31697454436694750733…62232995786092102401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.339 × 10⁹⁷(98-digit number)
63394908873389501466…24465991572184204801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.267 × 10⁹⁸(99-digit number)
12678981774677900293…48931983144368409601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.535 × 10⁹⁸(99-digit number)
25357963549355800586…97863966288736819201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.071 × 10⁹⁸(99-digit number)
50715927098711601173…95727932577473638401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.014 × 10⁹⁹(100-digit number)
10143185419742320234…91455865154947276801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.028 × 10⁹⁹(100-digit number)
20286370839484640469…82911730309894553601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.057 × 10⁹⁹(100-digit number)
40572741678969280938…65823460619789107201
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:57,857,881 XPM·at block #6,826,715 · updates every 60s
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