Block #1,487,166

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/7/2016, 7:06:33 AM · Difficulty 10.7207 · 5,337,779 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
48da3fdc927060c0555f2caf2ea7d0f5deeb3f522f0985f3320cb393a4d739fd

Height

#1,487,166

Difficulty

10.720689

Transactions

2

Size

1006 B

Version

2

Bits

0ab87f19

Nonce

87,082

Timestamp

3/7/2016, 7:06:33 AM

Confirmations

5,337,779

Merkle Root

50e1513a30fab10e317a0beafeaaeddf49027b0383033d91ac2b0d6981f5c6e7
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.

1.133 × 10⁹⁸(99-digit number)
11331964764903748674…72477397637437553281
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
1.133 × 10⁹⁸(99-digit number)
11331964764903748674…72477397637437553281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.266 × 10⁹⁸(99-digit number)
22663929529807497349…44954795274875106561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.532 × 10⁹⁸(99-digit number)
45327859059614994699…89909590549750213121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.065 × 10⁹⁸(99-digit number)
90655718119229989398…79819181099500426241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.813 × 10⁹⁹(100-digit number)
18131143623845997879…59638362199000852481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.626 × 10⁹⁹(100-digit number)
36262287247691995759…19276724398001704961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.252 × 10⁹⁹(100-digit number)
72524574495383991518…38553448796003409921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.450 × 10¹⁰⁰(101-digit number)
14504914899076798303…77106897592006819841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.900 × 10¹⁰⁰(101-digit number)
29009829798153596607…54213795184013639681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.801 × 10¹⁰⁰(101-digit number)
58019659596307193214…08427590368027279361
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:57,843,637 XPM·at block #6,824,944 · updates every 60s
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