Block #1,493,691

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/12/2016, 11:05:26 AM · Difficulty 10.6654 · 5,333,077 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ccad5bffaf5444921e4dc57ee1e71afda44fafef48c072b6e5ddaa2c8862ada4

Height

#1,493,691

Difficulty

10.665410

Transactions

2

Size

1.31 KB

Version

2

Bits

0aaa5847

Nonce

1,833,906,828

Timestamp

3/12/2016, 11:05:26 AM

Confirmations

5,333,077

Merkle Root

d5dccbeb36f8d95734c7829a76e7aa3fa68514de00c3c15d85bf345b08d3d9ac
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.

7.465 × 10⁹⁴(95-digit number)
74655635220817323049…22975543061368008201
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
7.465 × 10⁹⁴(95-digit number)
74655635220817323049…22975543061368008201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.493 × 10⁹⁵(96-digit number)
14931127044163464609…45951086122736016401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.986 × 10⁹⁵(96-digit number)
29862254088326929219…91902172245472032801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.972 × 10⁹⁵(96-digit number)
59724508176653858439…83804344490944065601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.194 × 10⁹⁶(97-digit number)
11944901635330771687…67608688981888131201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.388 × 10⁹⁶(97-digit number)
23889803270661543375…35217377963776262401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.777 × 10⁹⁶(97-digit number)
47779606541323086751…70434755927552524801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.555 × 10⁹⁶(97-digit number)
95559213082646173503…40869511855105049601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.911 × 10⁹⁷(98-digit number)
19111842616529234700…81739023710210099201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.822 × 10⁹⁷(98-digit number)
38223685233058469401…63478047420420198401
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:57,858,305 XPM·at block #6,826,767 · updates every 60s
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