Block #1,437,273

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/31/2016, 1:03:35 PM · Difficulty 10.7949 · 5,389,689 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
33c807c6b6c9bc12e4842c10a189769e932901ed28ae49f40c77bf7b761c2384

Height

#1,437,273

Difficulty

10.794861

Transactions

2

Size

1004 B

Version

2

Bits

0acb7c02

Nonce

1,416,567,848

Timestamp

1/31/2016, 1:03:35 PM

Confirmations

5,389,689

Merkle Root

6809d662626b828dafbf45d8be8c948524bff5a343a706b504cb69db4e3aa893
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.

1.308 × 10⁹⁶(97-digit number)
13086019953664303613…03692961472524163041
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
1.308 × 10⁹⁶(97-digit number)
13086019953664303613…03692961472524163041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.617 × 10⁹⁶(97-digit number)
26172039907328607226…07385922945048326081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.234 × 10⁹⁶(97-digit number)
52344079814657214453…14771845890096652161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.046 × 10⁹⁷(98-digit number)
10468815962931442890…29543691780193304321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.093 × 10⁹⁷(98-digit number)
20937631925862885781…59087383560386608641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.187 × 10⁹⁷(98-digit number)
41875263851725771562…18174767120773217281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.375 × 10⁹⁷(98-digit number)
83750527703451543125…36349534241546434561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.675 × 10⁹⁸(99-digit number)
16750105540690308625…72699068483092869121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.350 × 10⁹⁸(99-digit number)
33500211081380617250…45398136966185738241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.700 × 10⁹⁸(99-digit number)
67000422162761234500…90796273932371476481
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:57,859,872 XPM·at block #6,826,961 · updates every 60s
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