Block #390,463

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/5/2014, 4:37:48 AM · Difficulty 10.4229 · 6,419,330 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
343987e08e324a8bb12b0bf0c2e3aa5c0a75febcdd09bb81cf2d0146d44506b2

Height

#390,463

Difficulty

10.422904

Transactions

2

Size

392 B

Version

2

Bits

0a6c4374

Nonce

8,447,524

Timestamp

2/5/2014, 4:37:48 AM

Confirmations

6,419,330

Merkle Root

acb4c82e8f6019d8266fb35257e1a91b44c1efebb96169e7bcce748cfba44dd9
Transactions (2)
1 in → 1 out9.2000 XPM109 B
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.

2.964 × 10⁹⁴(95-digit number)
29641779478271596883…53090440392285909959
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
2.964 × 10⁹⁴(95-digit number)
29641779478271596883…53090440392285909959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.928 × 10⁹⁴(95-digit number)
59283558956543193766…06180880784571819919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.185 × 10⁹⁵(96-digit number)
11856711791308638753…12361761569143639839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.371 × 10⁹⁵(96-digit number)
23713423582617277506…24723523138287279679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.742 × 10⁹⁵(96-digit number)
47426847165234555013…49447046276574559359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.485 × 10⁹⁵(96-digit number)
94853694330469110027…98894092553149118719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.897 × 10⁹⁶(97-digit number)
18970738866093822005…97788185106298237439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.794 × 10⁹⁶(97-digit number)
37941477732187644010…95576370212596474879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.588 × 10⁹⁶(97-digit number)
75882955464375288021…91152740425192949759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.517 × 10⁹⁷(98-digit number)
15176591092875057604…82305480850385899519
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:57,722,424 XPM·at block #6,809,792 · updates every 60s
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