Block #1,219,261

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/2/2015, 11:38:04 PM · Difficulty 10.7283 · 5,611,242 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
83ddae1a8135c453f8ba31e78b2b1a3effcdfd5c7ebe27a6ed2ef739bddfcf60

Height

#1,219,261

Difficulty

10.728318

Transactions

2

Size

610 B

Version

2

Bits

0aba7307

Nonce

79,734,769

Timestamp

9/2/2015, 11:38:04 PM

Confirmations

5,611,242

Merkle Root

4af7a9aa1a443e5fd2d22ac3d72c542e24bd83a97900316bc0bc078395bdf81b
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.

2.333 × 10⁹⁴(95-digit number)
23337724708728249939…06052250549782528001
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
2.333 × 10⁹⁴(95-digit number)
23337724708728249939…06052250549782528001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.667 × 10⁹⁴(95-digit number)
46675449417456499879…12104501099565056001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.335 × 10⁹⁴(95-digit number)
93350898834912999759…24209002199130112001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.867 × 10⁹⁵(96-digit number)
18670179766982599951…48418004398260224001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.734 × 10⁹⁵(96-digit number)
37340359533965199903…96836008796520448001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.468 × 10⁹⁵(96-digit number)
74680719067930399807…93672017593040896001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.493 × 10⁹⁶(97-digit number)
14936143813586079961…87344035186081792001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.987 × 10⁹⁶(97-digit number)
29872287627172159923…74688070372163584001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.974 × 10⁹⁶(97-digit number)
59744575254344319846…49376140744327168001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.194 × 10⁹⁷(98-digit number)
11948915050868863969…98752281488654336001
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:57,888,274 XPM·at block #6,830,502 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy