Block #2,676,323

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/24/2018, 7:03:23 PM · Difficulty 11.6984 · 4,156,487 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3bec7d0ea4d6306b53c8de4dc8efb7e2d2c18a56fe2fdc6d60eb534585159c23

Height

#2,676,323

Difficulty

11.698417

Transactions

2

Size

575 B

Version

2

Bits

0bb2cb7b

Nonce

1,022,424,922

Timestamp

5/24/2018, 7:03:23 PM

Confirmations

4,156,487

Merkle Root

2b4c84da353a5fa69554d9b6de4f031b23ca7fa12a601778abb95324bbe6771e
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.

7.076 × 10⁹⁵(96-digit number)
70763455996255478771…13271870380563223041
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
7.076 × 10⁹⁵(96-digit number)
70763455996255478771…13271870380563223041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.415 × 10⁹⁶(97-digit number)
14152691199251095754…26543740761126446081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.830 × 10⁹⁶(97-digit number)
28305382398502191508…53087481522252892161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.661 × 10⁹⁶(97-digit number)
56610764797004383017…06174963044505784321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.132 × 10⁹⁷(98-digit number)
11322152959400876603…12349926089011568641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.264 × 10⁹⁷(98-digit number)
22644305918801753207…24699852178023137281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.528 × 10⁹⁷(98-digit number)
45288611837603506414…49399704356046274561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.057 × 10⁹⁷(98-digit number)
90577223675207012828…98799408712092549121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.811 × 10⁹⁸(99-digit number)
18115444735041402565…97598817424185098241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.623 × 10⁹⁸(99-digit number)
36230889470082805131…95197634848370196481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
7.246 × 10⁹⁸(99-digit number)
72461778940165610262…90395269696740392961
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:57,906,650 XPM·at block #6,832,809 · updates every 60s
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