Block #1,951,602

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/23/2017, 10:29:56 PM · Difficulty 10.7291 · 4,875,238 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
069fe6dc6e5ff05907ea996e9333a5b882caad2ae0943362d96c3696922bab24

Height

#1,951,602

Difficulty

10.729137

Transactions

3

Size

4.58 KB

Version

2

Bits

0abaa8c1

Nonce

1,028,872,571

Timestamp

1/23/2017, 10:29:56 PM

Confirmations

4,875,238

Merkle Root

86789b4a3ae57e787d4479c3c22ebeb0273adf984e0eda7be15cdb592cc8a721
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.

1.779 × 10⁹⁵(96-digit number)
17794499552472589520…55127194359612270081
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
1.779 × 10⁹⁵(96-digit number)
17794499552472589520…55127194359612270081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.558 × 10⁹⁵(96-digit number)
35588999104945179041…10254388719224540161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.117 × 10⁹⁵(96-digit number)
71177998209890358082…20508777438449080321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.423 × 10⁹⁶(97-digit number)
14235599641978071616…41017554876898160641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.847 × 10⁹⁶(97-digit number)
28471199283956143232…82035109753796321281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.694 × 10⁹⁶(97-digit number)
56942398567912286465…64070219507592642561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.138 × 10⁹⁷(98-digit number)
11388479713582457293…28140439015185285121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.277 × 10⁹⁷(98-digit number)
22776959427164914586…56280878030370570241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.555 × 10⁹⁷(98-digit number)
45553918854329829172…12561756060741140481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.110 × 10⁹⁷(98-digit number)
91107837708659658345…25123512121482280961
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:57,858,887 XPM·at block #6,826,839 · updates every 60s
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