Block #1,336,681

2CCLength 13★★★★★

Cunningham Chain of the Second Kind · Discovered 11/22/2015, 9:04:51 AM · Difficulty 10.8085 · 5,472,816 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
94d9ddd639a1da83d0e69279c804d26ea44fccafa94440a1747f540693e080f3

Height

#1,336,681

Difficulty

10.808473

Transactions

2

Size

970 B

Version

2

Bits

0acef812

Nonce

1,038,890,888

Timestamp

11/22/2015, 9:04:51 AM

Confirmations

5,472,816

Merkle Root

3c1cf02ae4b5bec727a11facd93480c88c66d405d3158174ab5d2df672c4fea9
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.

4.251 × 10⁹⁵(96-digit number)
42513383764075319104…12595974028413813761
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
4.251 × 10⁹⁵(96-digit number)
42513383764075319104…12595974028413813761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.502 × 10⁹⁵(96-digit number)
85026767528150638208…25191948056827627521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.700 × 10⁹⁶(97-digit number)
17005353505630127641…50383896113655255041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.401 × 10⁹⁶(97-digit number)
34010707011260255283…00767792227310510081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.802 × 10⁹⁶(97-digit number)
68021414022520510566…01535584454621020161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.360 × 10⁹⁷(98-digit number)
13604282804504102113…03071168909242040321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.720 × 10⁹⁷(98-digit number)
27208565609008204226…06142337818484080641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.441 × 10⁹⁷(98-digit number)
54417131218016408453…12284675636968161281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.088 × 10⁹⁸(99-digit number)
10883426243603281690…24569351273936322561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.176 × 10⁹⁸(99-digit number)
21766852487206563381…49138702547872645121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.353 × 10⁹⁸(99-digit number)
43533704974413126762…98277405095745290241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
12
2^11 × origin + 1
8.706 × 10⁹⁸(99-digit number)
87067409948826253525…96554810191490580481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
13
2^12 × origin + 1
1.741 × 10⁹⁹(100-digit number)
17413481989765250705…93109620382981160961
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 13 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
LegendaryChain length 13

Roughly 1 in 100,000 blocks. Extremely rare — celebrated by the community.

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:57,720,049 XPM·at block #6,809,496 · updates every 60s
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