Block #1,524,595

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/3/2016, 1:16:16 PM · Difficulty 10.6009 · 5,288,248 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
98033360100d0d2572f1dd8fd48f8c87172511f3cddd859e301dfa2c627fbaf6

Height

#1,524,595

Difficulty

10.600872

Transactions

5

Size

100.41 KB

Version

2

Bits

0a99d2b8

Nonce

210,502,724

Timestamp

4/3/2016, 1:16:16 PM

Confirmations

5,288,248

Merkle Root

4204b2cc2957f16e6ee7ac93ce7eb34f38da574ee91a306766478f38e06cb5ae
Transactions (5)
1 in → 1 out9.9300 XPM110 B
151 in → 1 out2.0000 XPM21.87 KB
152 in → 1 out2.0000 XPM22.00 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.

4.667 × 10⁹³(94-digit number)
46679872943562231143…38764831723359238401
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
4.667 × 10⁹³(94-digit number)
46679872943562231143…38764831723359238401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.335 × 10⁹³(94-digit number)
93359745887124462286…77529663446718476801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.867 × 10⁹⁴(95-digit number)
18671949177424892457…55059326893436953601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.734 × 10⁹⁴(95-digit number)
37343898354849784914…10118653786873907201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.468 × 10⁹⁴(95-digit number)
74687796709699569828…20237307573747814401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.493 × 10⁹⁵(96-digit number)
14937559341939913965…40474615147495628801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.987 × 10⁹⁵(96-digit number)
29875118683879827931…80949230294991257601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.975 × 10⁹⁵(96-digit number)
59750237367759655863…61898460589982515201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.195 × 10⁹⁶(97-digit number)
11950047473551931172…23796921179965030401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.390 × 10⁹⁶(97-digit number)
23900094947103862345…47593842359930060801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.780 × 10⁹⁶(97-digit number)
47800189894207724690…95187684719860121601
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:57,746,778 XPM·at block #6,812,842 · updates every 60s
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