Block #1,892,767

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/13/2016, 9:59:30 PM · Difficulty 10.7392 · 4,934,198 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4be4fe2e1180d164f2bcec47437c26f012a2d7b8d5433a2f78871fa29a0dddca

Height

#1,892,767

Difficulty

10.739209

Transactions

5

Size

7.40 KB

Version

2

Bits

0abd3ccc

Nonce

2,011,590,667

Timestamp

12/13/2016, 9:59:30 PM

Confirmations

4,934,198

Merkle Root

0fc25fe06ec0f99c8444d0a3f0017b5eb34eb91ea5d523d73964b0f5f90273c9
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.

3.516 × 10⁹⁴(95-digit number)
35166300493886881807…27682247739889300001
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
3.516 × 10⁹⁴(95-digit number)
35166300493886881807…27682247739889300001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.033 × 10⁹⁴(95-digit number)
70332600987773763615…55364495479778600001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.406 × 10⁹⁵(96-digit number)
14066520197554752723…10728990959557200001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.813 × 10⁹⁵(96-digit number)
28133040395109505446…21457981919114400001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.626 × 10⁹⁵(96-digit number)
56266080790219010892…42915963838228800001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.125 × 10⁹⁶(97-digit number)
11253216158043802178…85831927676457600001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.250 × 10⁹⁶(97-digit number)
22506432316087604356…71663855352915200001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.501 × 10⁹⁶(97-digit number)
45012864632175208713…43327710705830400001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.002 × 10⁹⁶(97-digit number)
90025729264350417427…86655421411660800001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.800 × 10⁹⁷(98-digit number)
18005145852870083485…73310842823321600001
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:57,859,897 XPM·at block #6,826,964 · updates every 60s
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