Block #932,310

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/11/2015, 8:20:24 PM · Difficulty 10.9026 · 5,894,038 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a88e3bc6dcfc63a301449c1756a70e6db4505bcbf5889e6102469f1c42603785

Height

#932,310

Difficulty

10.902580

Transactions

2

Size

1.79 KB

Version

2

Bits

0ae70f7a

Nonce

100,826,530

Timestamp

2/11/2015, 8:20:24 PM

Confirmations

5,894,038

Merkle Root

fb4ceae174a28604a0788dbd6b2bf7b1f8e519c9164267ef2951459d01c7f321
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.

2.499 × 10⁹⁵(96-digit number)
24997950163525552606…40755936573696567761
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
2.499 × 10⁹⁵(96-digit number)
24997950163525552606…40755936573696567761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.999 × 10⁹⁵(96-digit number)
49995900327051105212…81511873147393135521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.999 × 10⁹⁵(96-digit number)
99991800654102210424…63023746294786271041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.999 × 10⁹⁶(97-digit number)
19998360130820442084…26047492589572542081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.999 × 10⁹⁶(97-digit number)
39996720261640884169…52094985179145084161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.999 × 10⁹⁶(97-digit number)
79993440523281768339…04189970358290168321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.599 × 10⁹⁷(98-digit number)
15998688104656353667…08379940716580336641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.199 × 10⁹⁷(98-digit number)
31997376209312707335…16759881433160673281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.399 × 10⁹⁷(98-digit number)
63994752418625414671…33519762866321346561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.279 × 10⁹⁸(99-digit number)
12798950483725082934…67039525732642693121
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:57,854,928 XPM·at block #6,826,347 · updates every 60s
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