Block #1,523,728

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/2/2016, 10:33:16 PM · Difficulty 10.6020 · 5,293,454 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
617ef6c513ced40a8ed27f32445c04440100092310b8ef3ded57346a67fae84a

Height

#1,523,728

Difficulty

10.601990

Transactions

3

Size

3.89 KB

Version

2

Bits

0a9a1c0c

Nonce

1,161,438,537

Timestamp

4/2/2016, 10:33:16 PM

Confirmations

5,293,454

Merkle Root

dd4d6317b3bd1a07567e17ccb69bd51d1459c69ba59435e1c89b6aaa45ee66ae
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.

1.714 × 10⁹²(93-digit number)
17147756976216159065…21241799059814284481
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
1.714 × 10⁹²(93-digit number)
17147756976216159065…21241799059814284481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.429 × 10⁹²(93-digit number)
34295513952432318130…42483598119628568961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.859 × 10⁹²(93-digit number)
68591027904864636260…84967196239257137921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.371 × 10⁹³(94-digit number)
13718205580972927252…69934392478514275841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.743 × 10⁹³(94-digit number)
27436411161945854504…39868784957028551681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.487 × 10⁹³(94-digit number)
54872822323891709008…79737569914057103361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.097 × 10⁹⁴(95-digit number)
10974564464778341801…59475139828114206721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.194 × 10⁹⁴(95-digit number)
21949128929556683603…18950279656228413441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.389 × 10⁹⁴(95-digit number)
43898257859113367206…37900559312456826881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.779 × 10⁹⁴(95-digit number)
87796515718226734412…75801118624913653761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.755 × 10⁹⁵(96-digit number)
17559303143645346882…51602237249827307521
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:57,781,490 XPM·at block #6,817,181 · updates every 60s
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