1. #6,795,405TWN11 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #999,067

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/1/2015, 11:37:18 PM · Difficulty 10.7893 · 5,796,339 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
78e2d848d94ab1570b83b0bebc9d355cff9521f9a2ab84a4ce33ddacc2dc40b1

Height

#999,067

Difficulty

10.789301

Transactions

5

Size

1.22 KB

Version

2

Bits

0aca0f9b

Nonce

619,241,805

Timestamp

4/1/2015, 11:37:18 PM

Confirmations

5,796,339

Merkle Root

c940ade552f77f1aa615cfe6e1dbb47a5a2886f800bc04072e3e554f533728d0
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.

3.859 × 10⁹³(94-digit number)
38597077722626382213…39717489976670719121
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
3.859 × 10⁹³(94-digit number)
38597077722626382213…39717489976670719121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.719 × 10⁹³(94-digit number)
77194155445252764427…79434979953341438241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.543 × 10⁹⁴(95-digit number)
15438831089050552885…58869959906682876481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.087 × 10⁹⁴(95-digit number)
30877662178101105770…17739919813365752961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.175 × 10⁹⁴(95-digit number)
61755324356202211541…35479839626731505921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.235 × 10⁹⁵(96-digit number)
12351064871240442308…70959679253463011841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.470 × 10⁹⁵(96-digit number)
24702129742480884616…41919358506926023681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.940 × 10⁹⁵(96-digit number)
49404259484961769233…83838717013852047361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.880 × 10⁹⁵(96-digit number)
98808518969923538466…67677434027704094721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.976 × 10⁹⁶(97-digit number)
19761703793984707693…35354868055408189441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.952 × 10⁹⁶(97-digit number)
39523407587969415386…70709736110816378881
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:57,607,308 XPM·at block #6,795,405 · 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.