Block #485,280

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/10/2014, 11:33:37 PM · Difficulty 10.6060 · 6,331,300 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c783278aead602fdc4c09a71785ad4710d009c66a0934a63c5fa38574c363952

Height

#485,280

Difficulty

10.605952

Transactions

3

Size

660 B

Version

2

Bits

0a9b1fb1

Nonce

32,677,589

Timestamp

4/10/2014, 11:33:37 PM

Confirmations

6,331,300

Merkle Root

762bd381ef90ceae8449aaa60a96dc33b2d23342bffa4ef6b6bbcb76dfb4b4bc
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.

2.132 × 10⁹⁴(95-digit number)
21329845748859609057…81221295879551467109
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
2.132 × 10⁹⁴(95-digit number)
21329845748859609057…81221295879551467109
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.265 × 10⁹⁴(95-digit number)
42659691497719218115…62442591759102934219
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.531 × 10⁹⁴(95-digit number)
85319382995438436230…24885183518205868439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.706 × 10⁹⁵(96-digit number)
17063876599087687246…49770367036411736879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.412 × 10⁹⁵(96-digit number)
34127753198175374492…99540734072823473759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.825 × 10⁹⁵(96-digit number)
68255506396350748984…99081468145646947519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.365 × 10⁹⁶(97-digit number)
13651101279270149796…98162936291293895039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.730 × 10⁹⁶(97-digit number)
27302202558540299593…96325872582587790079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.460 × 10⁹⁶(97-digit number)
54604405117080599187…92651745165175580159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.092 × 10⁹⁷(98-digit number)
10920881023416119837…85303490330351160319
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:57,776,773 XPM·at block #6,816,579 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy