Block #1,606,512

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/30/2016, 10:08:18 AM · Difficulty 10.6071 · 5,224,725 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3f85dd9eaca89f488036c4ad2987f9e124323bcece8a59a2df7e21a703a247ae

Height

#1,606,512

Difficulty

10.607130

Transactions

3

Size

8.38 KB

Version

2

Bits

0a9b6ce7

Nonce

1,594,859,972

Timestamp

5/30/2016, 10:08:18 AM

Confirmations

5,224,725

Merkle Root

696eb018dd27637a39706aa1f7bca3ffcac4c134d3a14c380c384be1142fc596
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.

4.341 × 10⁹⁴(95-digit number)
43416335145904168184…79804356807072537561
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
4.341 × 10⁹⁴(95-digit number)
43416335145904168184…79804356807072537561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.683 × 10⁹⁴(95-digit number)
86832670291808336368…59608713614145075121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.736 × 10⁹⁵(96-digit number)
17366534058361667273…19217427228290150241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.473 × 10⁹⁵(96-digit number)
34733068116723334547…38434854456580300481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.946 × 10⁹⁵(96-digit number)
69466136233446669094…76869708913160600961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.389 × 10⁹⁶(97-digit number)
13893227246689333818…53739417826321201921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.778 × 10⁹⁶(97-digit number)
27786454493378667637…07478835652642403841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.557 × 10⁹⁶(97-digit number)
55572908986757335275…14957671305284807681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.111 × 10⁹⁷(98-digit number)
11114581797351467055…29915342610569615361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.222 × 10⁹⁷(98-digit number)
22229163594702934110…59830685221139230721
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:57,894,045 XPM·at block #6,831,236 · updates every 60s
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