Block #1,453,630

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/12/2016, 10:11:43 PM · Difficulty 10.7261 · 5,372,481 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
838d6174327ed11c7755b8c2dc940bcc6d7e9c883e2618a408a55f23db8d7c1b

Height

#1,453,630

Difficulty

10.726133

Transactions

2

Size

1.08 KB

Version

2

Bits

0ab9e3d3

Nonce

938,813,412

Timestamp

2/12/2016, 10:11:43 PM

Confirmations

5,372,481

Merkle Root

030d89bd3a2972d61ba23f5283d78dc73f21ec666a9255bd799ba36628afd1fb
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.

8.831 × 10⁹³(94-digit number)
88310228728060409853…47239397995129786879
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
8.831 × 10⁹³(94-digit number)
88310228728060409853…47239397995129786879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.766 × 10⁹⁴(95-digit number)
17662045745612081970…94478795990259573759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.532 × 10⁹⁴(95-digit number)
35324091491224163941…88957591980519147519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.064 × 10⁹⁴(95-digit number)
70648182982448327882…77915183961038295039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.412 × 10⁹⁵(96-digit number)
14129636596489665576…55830367922076590079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.825 × 10⁹⁵(96-digit number)
28259273192979331153…11660735844153180159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.651 × 10⁹⁵(96-digit number)
56518546385958662306…23321471688306360319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.130 × 10⁹⁶(97-digit number)
11303709277191732461…46642943376612720639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.260 × 10⁹⁶(97-digit number)
22607418554383464922…93285886753225441279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.521 × 10⁹⁶(97-digit number)
45214837108766929844…86571773506450882559
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:57,853,012 XPM·at block #6,826,110 · updates every 60s
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