Block #1,990,456

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/19/2017, 8:38:50 PM · Difficulty 10.7351 · 4,850,567 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
752e7207fc87fbe6beb7b4af0ddd8440a35940007079d2ef7778640ac94536d8

Height

#1,990,456

Difficulty

10.735065

Transactions

2

Size

424 B

Version

2

Bits

0abc2d3d

Nonce

584,428,747

Timestamp

2/19/2017, 8:38:50 PM

Confirmations

4,850,567

Merkle Root

5504c9d4bb34905af9d61972963c95e2ac1416aad30bbe3b9bd679b73e04edf0
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.

3.507 × 10⁹¹(92-digit number)
35078913228493852709…27031445517329108959
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
3.507 × 10⁹¹(92-digit number)
35078913228493852709…27031445517329108959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.015 × 10⁹¹(92-digit number)
70157826456987705418…54062891034658217919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.403 × 10⁹²(93-digit number)
14031565291397541083…08125782069316435839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.806 × 10⁹²(93-digit number)
28063130582795082167…16251564138632871679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.612 × 10⁹²(93-digit number)
56126261165590164334…32503128277265743359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.122 × 10⁹³(94-digit number)
11225252233118032866…65006256554531486719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.245 × 10⁹³(94-digit number)
22450504466236065733…30012513109062973439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.490 × 10⁹³(94-digit number)
44901008932472131467…60025026218125946879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.980 × 10⁹³(94-digit number)
89802017864944262935…20050052436251893759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.796 × 10⁹⁴(95-digit number)
17960403572988852587…40100104872503787519
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:57,972,541 XPM·at block #6,841,022 · updates every 60s
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