Block #1,263,650

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/2/2015, 7:44:51 AM · Difficulty 10.8235 · 5,541,631 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
17b208a2f5fc1a31de9ff27f523945e683a6517e909c1c23e1f8f13aa827abf5

Height

#1,263,650

Difficulty

10.823539

Transactions

2

Size

427 B

Version

2

Bits

0ad2d378

Nonce

480,930,586

Timestamp

10/2/2015, 7:44:51 AM

Confirmations

5,541,631

Merkle Root

8c4a8ac23f5652f6efe5397e85b2ae25d0ed65f35940d0de34dcb4f62a8688e9
Transactions (2)
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.

2.512 × 10⁹⁶(97-digit number)
25127575257735952144…78175954952810636801
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
2.512 × 10⁹⁶(97-digit number)
25127575257735952144…78175954952810636801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.025 × 10⁹⁶(97-digit number)
50255150515471904288…56351909905621273601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.005 × 10⁹⁷(98-digit number)
10051030103094380857…12703819811242547201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.010 × 10⁹⁷(98-digit number)
20102060206188761715…25407639622485094401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.020 × 10⁹⁷(98-digit number)
40204120412377523431…50815279244970188801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.040 × 10⁹⁷(98-digit number)
80408240824755046862…01630558489940377601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.608 × 10⁹⁸(99-digit number)
16081648164951009372…03261116979880755201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.216 × 10⁹⁸(99-digit number)
32163296329902018744…06522233959761510401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.432 × 10⁹⁸(99-digit number)
64326592659804037489…13044467919523020801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.286 × 10⁹⁹(100-digit number)
12865318531960807497…26088935839046041601
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:57,686,321 XPM·at block #6,805,280 · updates every 60s
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