Block #1,602,668

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/27/2016, 8:56:28 PM · Difficulty 10.5933 · 5,213,714 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a32726b20596e45d2b89177d8823af83904e71b62844b8c966a76e4cd471278e

Height

#1,602,668

Difficulty

10.593335

Transactions

2

Size

561 B

Version

2

Bits

0a97e4d2

Nonce

580,574,109

Timestamp

5/27/2016, 8:56:28 PM

Confirmations

5,213,714

Merkle Root

84ec52d005b667d62115cdf486af233fc8de0ab44dc9b42cd443a35432d1a768
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.

1.301 × 10⁹²(93-digit number)
13019117795760406690…28446298100920595201
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
1.301 × 10⁹²(93-digit number)
13019117795760406690…28446298100920595201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.603 × 10⁹²(93-digit number)
26038235591520813381…56892596201841190401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.207 × 10⁹²(93-digit number)
52076471183041626763…13785192403682380801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.041 × 10⁹³(94-digit number)
10415294236608325352…27570384807364761601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.083 × 10⁹³(94-digit number)
20830588473216650705…55140769614729523201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.166 × 10⁹³(94-digit number)
41661176946433301410…10281539229459046401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.332 × 10⁹³(94-digit number)
83322353892866602821…20563078458918092801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.666 × 10⁹⁴(95-digit number)
16664470778573320564…41126156917836185601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.332 × 10⁹⁴(95-digit number)
33328941557146641128…82252313835672371201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.665 × 10⁹⁴(95-digit number)
66657883114293282256…64504627671344742401
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:57,775,185 XPM·at block #6,816,381 · updates every 60s
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