Block #1,464,450

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/19/2016, 4:44:12 PM · Difficulty 10.7786 · 5,350,694 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
80e3a8e6cf53a090e278a377e5d2fb872fab11f65b67c1682a4b1d0217837b0b

Height

#1,464,450

Difficulty

10.778572

Transactions

2

Size

631 B

Version

2

Bits

0ac75077

Nonce

734,374,070

Timestamp

2/19/2016, 4:44:12 PM

Confirmations

5,350,694

Merkle Root

eebee5afdb82f9ab1b210442575e85f39740fd4bebf7a6d272cd5c94043800ba
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.

1.498 × 10⁹⁵(96-digit number)
14985385169389496736…35852459050541419519
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
1.498 × 10⁹⁵(96-digit number)
14985385169389496736…35852459050541419519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.997 × 10⁹⁵(96-digit number)
29970770338778993473…71704918101082839039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.994 × 10⁹⁵(96-digit number)
59941540677557986946…43409836202165678079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.198 × 10⁹⁶(97-digit number)
11988308135511597389…86819672404331356159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.397 × 10⁹⁶(97-digit number)
23976616271023194778…73639344808662712319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.795 × 10⁹⁶(97-digit number)
47953232542046389556…47278689617325424639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.590 × 10⁹⁶(97-digit number)
95906465084092779113…94557379234650849279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.918 × 10⁹⁷(98-digit number)
19181293016818555822…89114758469301698559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.836 × 10⁹⁷(98-digit number)
38362586033637111645…78229516938603397119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.672 × 10⁹⁷(98-digit number)
76725172067274223290…56459033877206794239
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:57,765,246 XPM·at block #6,815,143 · updates every 60s
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