Block #1,480,440

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/2/2016, 3:40:57 PM · Difficulty 10.7182 · 5,336,093 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
523219508e29a9acf4d13fbbb46a50e7c481c9dd749191151338e187667ed3d4

Height

#1,480,440

Difficulty

10.718163

Transactions

2

Size

1.28 KB

Version

2

Bits

0ab7d986

Nonce

480,652,575

Timestamp

3/2/2016, 3:40:57 PM

Confirmations

5,336,093

Merkle Root

7f3d4707802bb213abf0671ef64007f378b53adac54d16a641109c9bab849d2f
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.

3.670 × 10⁹⁴(95-digit number)
36700653402422229451…46583115306797854399
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
3.670 × 10⁹⁴(95-digit number)
36700653402422229451…46583115306797854399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.340 × 10⁹⁴(95-digit number)
73401306804844458903…93166230613595708799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.468 × 10⁹⁵(96-digit number)
14680261360968891780…86332461227191417599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.936 × 10⁹⁵(96-digit number)
29360522721937783561…72664922454382835199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.872 × 10⁹⁵(96-digit number)
58721045443875567122…45329844908765670399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.174 × 10⁹⁶(97-digit number)
11744209088775113424…90659689817531340799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.348 × 10⁹⁶(97-digit number)
23488418177550226849…81319379635062681599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.697 × 10⁹⁶(97-digit number)
46976836355100453698…62638759270125363199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.395 × 10⁹⁶(97-digit number)
93953672710200907396…25277518540250726399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.879 × 10⁹⁷(98-digit number)
18790734542040181479…50555037080501452799
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:57,776,391 XPM·at block #6,816,532 · updates every 60s
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