Block #2,160,025

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/14/2017, 6:42:19 AM · Difficulty 10.9026 · 4,681,418 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2b0d123db1a99b9ef1ea656450ef1d8ead814af65ad8974664eb802866362762

Height

#2,160,025

Difficulty

10.902567

Transactions

2

Size

867 B

Version

2

Bits

0ae70e9a

Nonce

490,741,392

Timestamp

6/14/2017, 6:42:19 AM

Confirmations

4,681,418

Merkle Root

91c75c5160ba35f04acc4fa3c0f8601f6ce34c92544147d8ee7456478a60b3ae
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.

4.156 × 10⁹⁴(95-digit number)
41569452782310020261…42214354131227522369
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
4.156 × 10⁹⁴(95-digit number)
41569452782310020261…42214354131227522369
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.313 × 10⁹⁴(95-digit number)
83138905564620040523…84428708262455044739
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.662 × 10⁹⁵(96-digit number)
16627781112924008104…68857416524910089479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.325 × 10⁹⁵(96-digit number)
33255562225848016209…37714833049820178959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.651 × 10⁹⁵(96-digit number)
66511124451696032419…75429666099640357919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.330 × 10⁹⁶(97-digit number)
13302224890339206483…50859332199280715839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.660 × 10⁹⁶(97-digit number)
26604449780678412967…01718664398561431679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.320 × 10⁹⁶(97-digit number)
53208899561356825935…03437328797122863359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.064 × 10⁹⁷(98-digit number)
10641779912271365187…06874657594245726719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.128 × 10⁹⁷(98-digit number)
21283559824542730374…13749315188491453439
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,975,924 XPM·at block #6,841,442 · updates every 60s
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