Block #606,034

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/28/2014, 11:35:10 PM · Difficulty 10.9088 · 6,190,705 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a9d1e0870b7556193d9ed4e733fdee74c4830baccc3cd1ab7afceae1ff490181

Height

#606,034

Difficulty

10.908754

Transactions

4

Size

850 B

Version

2

Bits

0ae8a412

Nonce

461,862,360

Timestamp

6/28/2014, 11:35:10 PM

Confirmations

6,190,705

Merkle Root

ca0dfc6fbb344c0ffe6e69ae5899055afdb40f6c7bb0ef478bcfa9966c0ea257
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.

1.657 × 10⁹⁹(100-digit number)
16577991144315975140…67495972391771522561
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
1.657 × 10⁹⁹(100-digit number)
16577991144315975140…67495972391771522561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.315 × 10⁹⁹(100-digit number)
33155982288631950281…34991944783543045121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.631 × 10⁹⁹(100-digit number)
66311964577263900563…69983889567086090241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.326 × 10¹⁰⁰(101-digit number)
13262392915452780112…39967779134172180481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.652 × 10¹⁰⁰(101-digit number)
26524785830905560225…79935558268344360961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.304 × 10¹⁰⁰(101-digit number)
53049571661811120450…59871116536688721921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.060 × 10¹⁰¹(102-digit number)
10609914332362224090…19742233073377443841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.121 × 10¹⁰¹(102-digit number)
21219828664724448180…39484466146754887681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.243 × 10¹⁰¹(102-digit number)
42439657329448896360…78968932293509775361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.487 × 10¹⁰¹(102-digit number)
84879314658897792720…57937864587019550721
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:57,617,920 XPM·at block #6,796,738 · updates every 60s
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