Block #1,977,345

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/10/2017, 10:18:03 AM · Difficulty 10.7582 · 4,849,651 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9cc13fbcce4bc7fb584aa11f1e527c9d71fcb7ede0a31cdb0130a9a3d5268cbc

Height

#1,977,345

Difficulty

10.758190

Transactions

2

Size

1019 B

Version

2

Bits

0ac218be

Nonce

111,367,602

Timestamp

2/10/2017, 10:18:03 AM

Confirmations

4,849,651

Merkle Root

fbcf5c8b3ae2e0cbd0388b576bce5c97c098f7657e6b6368067e42dd7d14c220
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.

1.718 × 10⁹⁴(95-digit number)
17187583716230089904…32339515166725130439
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
1.718 × 10⁹⁴(95-digit number)
17187583716230089904…32339515166725130439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.437 × 10⁹⁴(95-digit number)
34375167432460179809…64679030333450260879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.875 × 10⁹⁴(95-digit number)
68750334864920359619…29358060666900521759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.375 × 10⁹⁵(96-digit number)
13750066972984071923…58716121333801043519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.750 × 10⁹⁵(96-digit number)
27500133945968143847…17432242667602087039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.500 × 10⁹⁵(96-digit number)
55000267891936287695…34864485335204174079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.100 × 10⁹⁶(97-digit number)
11000053578387257539…69728970670408348159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.200 × 10⁹⁶(97-digit number)
22000107156774515078…39457941340816696319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.400 × 10⁹⁶(97-digit number)
44000214313549030156…78915882681633392639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.800 × 10⁹⁶(97-digit number)
88000428627098060313…57831765363266785279
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:57,860,144 XPM·at block #6,826,995 · updates every 60s
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