Block #1,889,514

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/11/2016, 7:25:44 PM · Difficulty 10.7274 · 4,952,703 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0dcfd96bd612aaf5227c982082cc7ac11187c1f9ac67a91004c689f5211b7aa5

Height

#1,889,514

Difficulty

10.727385

Transactions

2

Size

1.14 KB

Version

2

Bits

0aba35e5

Nonce

1,213,624,850

Timestamp

12/11/2016, 7:25:44 PM

Confirmations

4,952,703

Merkle Root

1364576be920b2c9dd008695cd95996731f57d9ed8bcfe244d4bd8df796a8dd0
Transactions (2)
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.

1.915 × 10⁹³(94-digit number)
19150828086506527581…84391820040491687041
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
1.915 × 10⁹³(94-digit number)
19150828086506527581…84391820040491687041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.830 × 10⁹³(94-digit number)
38301656173013055162…68783640080983374081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.660 × 10⁹³(94-digit number)
76603312346026110325…37567280161966748161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.532 × 10⁹⁴(95-digit number)
15320662469205222065…75134560323933496321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.064 × 10⁹⁴(95-digit number)
30641324938410444130…50269120647866992641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.128 × 10⁹⁴(95-digit number)
61282649876820888260…00538241295733985281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.225 × 10⁹⁵(96-digit number)
12256529975364177652…01076482591467970561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.451 × 10⁹⁵(96-digit number)
24513059950728355304…02152965182935941121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.902 × 10⁹⁵(96-digit number)
49026119901456710608…04305930365871882241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.805 × 10⁹⁵(96-digit number)
98052239802913421216…08611860731743764481
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:57,982,134 XPM·at block #6,842,216 · updates every 60s
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