Block #1,304,104

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/29/2015, 7:02:19 PM · Difficulty 10.8534 · 5,520,803 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
73f891520db0b7b9bb668520f3973c8bfb888acc1f3730409bde67a91eee70bf

Height

#1,304,104

Difficulty

10.853446

Transactions

2

Size

867 B

Version

2

Bits

0ada7b6f

Nonce

376,334,185

Timestamp

10/29/2015, 7:02:19 PM

Confirmations

5,520,803

Merkle Root

da8a7831367f5f07d1dcf43b83739534fda03794bf5051f4cd2335e88a9afaba
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.

1.922 × 10⁹⁴(95-digit number)
19229094144929279077…49368094768586504379
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
1.922 × 10⁹⁴(95-digit number)
19229094144929279077…49368094768586504379
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.845 × 10⁹⁴(95-digit number)
38458188289858558154…98736189537173008759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.691 × 10⁹⁴(95-digit number)
76916376579717116308…97472379074346017519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.538 × 10⁹⁵(96-digit number)
15383275315943423261…94944758148692035039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.076 × 10⁹⁵(96-digit number)
30766550631886846523…89889516297384070079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.153 × 10⁹⁵(96-digit number)
61533101263773693046…79779032594768140159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.230 × 10⁹⁶(97-digit number)
12306620252754738609…59558065189536280319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.461 × 10⁹⁶(97-digit number)
24613240505509477218…19116130379072560639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.922 × 10⁹⁶(97-digit number)
49226481011018954437…38232260758145121279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.845 × 10⁹⁶(97-digit number)
98452962022037908874…76464521516290242559
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:57,843,332 XPM·at block #6,824,906 · updates every 60s
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