Block #1,315,225

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/6/2015, 8:02:39 AM · Difficulty 10.8612 · 5,499,628 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c9f69d5ef4a8ad041e836cee2ecfe13a4aacd5d39097d59211eb17f3a0e3d904

Height

#1,315,225

Difficulty

10.861166

Transactions

2

Size

800 B

Version

2

Bits

0adc7560

Nonce

7,367,963

Timestamp

11/6/2015, 8:02:39 AM

Confirmations

5,499,628

Merkle Root

02d6748a234f8ec3cfb35d12ccc7c5494247a40feb94795e1d77916650fbc9ee
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.

3.147 × 10⁹⁵(96-digit number)
31471664595699733972…28724609160366549761
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
3.147 × 10⁹⁵(96-digit number)
31471664595699733972…28724609160366549761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.294 × 10⁹⁵(96-digit number)
62943329191399467945…57449218320733099521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.258 × 10⁹⁶(97-digit number)
12588665838279893589…14898436641466199041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.517 × 10⁹⁶(97-digit number)
25177331676559787178…29796873282932398081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.035 × 10⁹⁶(97-digit number)
50354663353119574356…59593746565864796161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.007 × 10⁹⁷(98-digit number)
10070932670623914871…19187493131729592321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.014 × 10⁹⁷(98-digit number)
20141865341247829742…38374986263459184641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.028 × 10⁹⁷(98-digit number)
40283730682495659484…76749972526918369281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.056 × 10⁹⁷(98-digit number)
80567461364991318969…53499945053836738561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.611 × 10⁹⁸(99-digit number)
16113492272998263793…06999890107673477121
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:57,762,907 XPM·at block #6,814,852 · updates every 60s
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