Block #794,536

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/2/2014, 11:28:29 PM · Difficulty 10.9750 · 6,001,200 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f382f82b686f92bc2c4f68cb1a777f6716aa79868e936791b918cf2fcab45996

Height

#794,536

Difficulty

10.974992

Transactions

5

Size

1.52 KB

Version

2

Bits

0af9990c

Nonce

630,794,655

Timestamp

11/2/2014, 11:28:29 PM

Confirmations

6,001,200

Merkle Root

0ee6b334e5fa440aa83a09db61cfe608cfbda4ba1b2e36fdc6ca9dfb0849782c
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.

3.872 × 10⁹⁵(96-digit number)
38721169251219490899…97139346653912305281
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
3.872 × 10⁹⁵(96-digit number)
38721169251219490899…97139346653912305281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.744 × 10⁹⁵(96-digit number)
77442338502438981798…94278693307824610561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.548 × 10⁹⁶(97-digit number)
15488467700487796359…88557386615649221121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.097 × 10⁹⁶(97-digit number)
30976935400975592719…77114773231298442241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.195 × 10⁹⁶(97-digit number)
61953870801951185438…54229546462596884481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.239 × 10⁹⁷(98-digit number)
12390774160390237087…08459092925193768961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.478 × 10⁹⁷(98-digit number)
24781548320780474175…16918185850387537921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.956 × 10⁹⁷(98-digit number)
49563096641560948351…33836371700775075841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.912 × 10⁹⁷(98-digit number)
99126193283121896702…67672743401550151681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.982 × 10⁹⁸(99-digit number)
19825238656624379340…35345486803100303361
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:57,609,965 XPM·at block #6,795,735 · updates every 60s
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