1. #6,826,571TWN11 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #2,282,015

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/4/2017, 11:20:36 AM · Difficulty 10.9557 · 4,544,557 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fd0c6e6874441efada4b7f083d15258ca3c290da798e9df2464235649b272a49

Height

#2,282,015

Difficulty

10.955670

Transactions

2

Size

574 B

Version

2

Bits

0af4a6d1

Nonce

1,093,814,047

Timestamp

9/4/2017, 11:20:36 AM

Confirmations

4,544,557

Merkle Root

f86362335da7f875ff4c6a6bf889f0af035be387a9e0eb837105aea9d23b073d
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.

3.043 × 10⁹⁴(95-digit number)
30431753058738372337…73889471751077649359
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
3.043 × 10⁹⁴(95-digit number)
30431753058738372337…73889471751077649359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.086 × 10⁹⁴(95-digit number)
60863506117476744675…47778943502155298719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.217 × 10⁹⁵(96-digit number)
12172701223495348935…95557887004310597439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.434 × 10⁹⁵(96-digit number)
24345402446990697870…91115774008621194879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.869 × 10⁹⁵(96-digit number)
48690804893981395740…82231548017242389759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.738 × 10⁹⁵(96-digit number)
97381609787962791480…64463096034484779519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.947 × 10⁹⁶(97-digit number)
19476321957592558296…28926192068969559039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.895 × 10⁹⁶(97-digit number)
38952643915185116592…57852384137939118079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.790 × 10⁹⁶(97-digit number)
77905287830370233184…15704768275878236159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.558 × 10⁹⁷(98-digit number)
15581057566074046636…31409536551756472319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.116 × 10⁹⁷(98-digit number)
31162115132148093273…62819073103512944639
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,856,725 XPM·at block #6,826,571 · updates every 60s
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