Block #1,534,394

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2016, 5:11:12 AM · Difficulty 10.6175 · 5,292,922 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fbf5877a2f9327da9a535fdd084d2bca391655d14328ffa95e47374618c46fd9

Height

#1,534,394

Difficulty

10.617535

Transactions

3

Size

15.00 KB

Version

2

Bits

0a9e16be

Nonce

1,228,976,782

Timestamp

4/10/2016, 5:11:12 AM

Confirmations

5,292,922

Merkle Root

924263286c8bb00e0585825f05f5c9cc548204ab20e7d246f6686d78f98f212c
Transactions (3)
1 in → 1 out9.0200 XPM110 B
51 in → 1 out206.2892 XPM7.40 KB
51 in → 1 out2703.3434 XPM7.41 KB
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.

1.346 × 10⁹³(94-digit number)
13467362149641314046…01507904579043946881
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
1.346 × 10⁹³(94-digit number)
13467362149641314046…01507904579043946881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.693 × 10⁹³(94-digit number)
26934724299282628093…03015809158087893761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.386 × 10⁹³(94-digit number)
53869448598565256186…06031618316175787521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.077 × 10⁹⁴(95-digit number)
10773889719713051237…12063236632351575041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.154 × 10⁹⁴(95-digit number)
21547779439426102474…24126473264703150081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.309 × 10⁹⁴(95-digit number)
43095558878852204949…48252946529406300161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.619 × 10⁹⁴(95-digit number)
86191117757704409899…96505893058812600321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.723 × 10⁹⁵(96-digit number)
17238223551540881979…93011786117625200641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.447 × 10⁹⁵(96-digit number)
34476447103081763959…86023572235250401281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.895 × 10⁹⁵(96-digit number)
68952894206163527919…72047144470500802561
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:57,862,641 XPM·at block #6,827,315 · updates every 60s
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