Block #1,976,603

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/9/2017, 9:49:55 PM · Difficulty 10.7585 · 4,860,407 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8b25fdfa38a562a93ecc2e3a14cd4e6f9fc8e813aabbd8ee3a07c94553ce58fd

Height

#1,976,603

Difficulty

10.758535

Transactions

2

Size

1.28 KB

Version

2

Bits

0ac22f5c

Nonce

1,415,032,416

Timestamp

2/9/2017, 9:49:55 PM

Confirmations

4,860,407

Merkle Root

1cc471bc6197f9db51bf75182699139f4dc965d8e955a5318d0af439ed458ed3
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.

2.483 × 10⁹⁴(95-digit number)
24830588696216579793…12393637961657864801
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
2.483 × 10⁹⁴(95-digit number)
24830588696216579793…12393637961657864801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.966 × 10⁹⁴(95-digit number)
49661177392433159586…24787275923315729601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.932 × 10⁹⁴(95-digit number)
99322354784866319172…49574551846631459201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.986 × 10⁹⁵(96-digit number)
19864470956973263834…99149103693262918401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.972 × 10⁹⁵(96-digit number)
39728941913946527669…98298207386525836801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.945 × 10⁹⁵(96-digit number)
79457883827893055338…96596414773051673601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.589 × 10⁹⁶(97-digit number)
15891576765578611067…93192829546103347201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.178 × 10⁹⁶(97-digit number)
31783153531157222135…86385659092206694401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.356 × 10⁹⁶(97-digit number)
63566307062314444270…72771318184413388801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.271 × 10⁹⁷(98-digit number)
12713261412462888854…45542636368826777601
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,940,376 XPM·at block #6,837,009 · updates every 60s
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