Block #2,680,928

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/28/2018, 1:29:40 AM · Difficulty 11.6926 · 4,160,400 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b9000669bede6b5ca85fe4f7de797b153c5a2b58f087e559be24d82cf9b90390

Height

#2,680,928

Difficulty

11.692637

Transactions

4

Size

808 B

Version

2

Bits

0bb150af

Nonce

668,404,450

Timestamp

5/28/2018, 1:29:40 AM

Confirmations

4,160,400

Merkle Root

29d63d9ed32fc55d89bb757276a54a461fe8d52170761de635b4055c86760367
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.

9.722 × 10⁹³(94-digit number)
97221514593053372246…22566151153353694721
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
9.722 × 10⁹³(94-digit number)
97221514593053372246…22566151153353694721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.944 × 10⁹⁴(95-digit number)
19444302918610674449…45132302306707389441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.888 × 10⁹⁴(95-digit number)
38888605837221348898…90264604613414778881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.777 × 10⁹⁴(95-digit number)
77777211674442697796…80529209226829557761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.555 × 10⁹⁵(96-digit number)
15555442334888539559…61058418453659115521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.111 × 10⁹⁵(96-digit number)
31110884669777079118…22116836907318231041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.222 × 10⁹⁵(96-digit number)
62221769339554158237…44233673814636462081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.244 × 10⁹⁶(97-digit number)
12444353867910831647…88467347629272924161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.488 × 10⁹⁶(97-digit number)
24888707735821663295…76934695258545848321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.977 × 10⁹⁶(97-digit number)
49777415471643326590…53869390517091696641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
9.955 × 10⁹⁶(97-digit number)
99554830943286653180…07738781034183393281
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:57,974,987 XPM·at block #6,841,327 · updates every 60s
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