Block #2,833,086

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/10/2018, 12:28:11 PM · Difficulty 11.7148 · 4,005,787 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a4b1359b0a2dfc5a05b6525516ec33bd3d59bde00d5fd407fe5ca85e06daeaec

Height

#2,833,086

Difficulty

11.714807

Transactions

2

Size

428 B

Version

2

Bits

0bb6fd9e

Nonce

606,431,489

Timestamp

9/10/2018, 12:28:11 PM

Confirmations

4,005,787

Merkle Root

5a634f6402c9fae9d6b486afa5fefe45776acee72cccbea2671a4d97e0fba55c
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.

1.837 × 10⁹⁶(97-digit number)
18376339542617494119…78716952073690101761
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
1.837 × 10⁹⁶(97-digit number)
18376339542617494119…78716952073690101761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.675 × 10⁹⁶(97-digit number)
36752679085234988238…57433904147380203521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.350 × 10⁹⁶(97-digit number)
73505358170469976476…14867808294760407041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.470 × 10⁹⁷(98-digit number)
14701071634093995295…29735616589520814081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.940 × 10⁹⁷(98-digit number)
29402143268187990590…59471233179041628161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.880 × 10⁹⁷(98-digit number)
58804286536375981181…18942466358083256321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.176 × 10⁹⁸(99-digit number)
11760857307275196236…37884932716166512641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.352 × 10⁹⁸(99-digit number)
23521714614550392472…75769865432333025281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.704 × 10⁹⁸(99-digit number)
47043429229100784945…51539730864666050561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.408 × 10⁹⁸(99-digit number)
94086858458201569890…03079461729332101121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.881 × 10⁹⁹(100-digit number)
18817371691640313978…06158923458664202241
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,955,250 XPM·at block #6,838,872 · updates every 60s
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