Block #1,966,077

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/2/2017, 4:22:26 PM · Difficulty 10.7524 · 4,877,327 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d40066fe869373191266d5564035f8c0048de4d45458eb89be39754a2dfc20da

Height

#1,966,077

Difficulty

10.752373

Transactions

3

Size

42.28 KB

Version

2

Bits

0ac09b80

Nonce

26,775,702

Timestamp

2/2/2017, 4:22:26 PM

Confirmations

4,877,327

Merkle Root

077a94806de6eb33212635430ff6d9f90ed321f58ed8c277f1fca5888270ff27
Transactions (3)
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.

6.316 × 10⁹³(94-digit number)
63167794024376975370…46752772041785498881
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
6.316 × 10⁹³(94-digit number)
63167794024376975370…46752772041785498881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.263 × 10⁹⁴(95-digit number)
12633558804875395074…93505544083570997761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.526 × 10⁹⁴(95-digit number)
25267117609750790148…87011088167141995521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.053 × 10⁹⁴(95-digit number)
50534235219501580296…74022176334283991041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.010 × 10⁹⁵(96-digit number)
10106847043900316059…48044352668567982081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.021 × 10⁹⁵(96-digit number)
20213694087800632118…96088705337135964161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.042 × 10⁹⁵(96-digit number)
40427388175601264237…92177410674271928321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.085 × 10⁹⁵(96-digit number)
80854776351202528474…84354821348543856641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.617 × 10⁹⁶(97-digit number)
16170955270240505694…68709642697087713281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.234 × 10⁹⁶(97-digit number)
32341910540481011389…37419285394175426561
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:57,991,598 XPM·at block #6,843,403 · updates every 60s
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