Block #1,491,848

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/11/2016, 12:05:20 AM · Difficulty 10.6820 · 5,349,726 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3756cd3ca9f0ce1df05e6a95e9c1dc0f796e7400e746932e57ea443c08da1bd8

Height

#1,491,848

Difficulty

10.681979

Transactions

2

Size

1.28 KB

Version

2

Bits

0aae9630

Nonce

1,678,969,025

Timestamp

3/11/2016, 12:05:20 AM

Confirmations

5,349,726

Merkle Root

1bfd3dafbe4eca003f15ffa7a9d0edf8f2e85e24c80a33b8b623c97d5345285c
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.

2.868 × 10⁹⁷(98-digit number)
28682858177607047473…81144574893996001281
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
2.868 × 10⁹⁷(98-digit number)
28682858177607047473…81144574893996001281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.736 × 10⁹⁷(98-digit number)
57365716355214094946…62289149787992002561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.147 × 10⁹⁸(99-digit number)
11473143271042818989…24578299575984005121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.294 × 10⁹⁸(99-digit number)
22946286542085637978…49156599151968010241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.589 × 10⁹⁸(99-digit number)
45892573084171275957…98313198303936020481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.178 × 10⁹⁸(99-digit number)
91785146168342551914…96626396607872040961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.835 × 10⁹⁹(100-digit number)
18357029233668510382…93252793215744081921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.671 × 10⁹⁹(100-digit number)
36714058467337020765…86505586431488163841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.342 × 10⁹⁹(100-digit number)
73428116934674041531…73011172862976327681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.468 × 10¹⁰⁰(101-digit number)
14685623386934808306…46022345725952655361
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:57,976,977 XPM·at block #6,841,573 · updates every 60s
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