Block #946,396

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/21/2015, 7:01:29 PM · Difficulty 10.8989 · 5,859,716 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dd6489379e34424b37df3e229370104086267df78d161a44f34fc8891e1b4348

Height

#946,396

Difficulty

10.898850

Transactions

5

Size

5.28 KB

Version

2

Bits

0ae61b0f

Nonce

170,226,292

Timestamp

2/21/2015, 7:01:29 PM

Confirmations

5,859,716

Merkle Root

08e7f525e5d47ac997f4f42f5f73ea67170af6aa64eefbd54f294ff020b40b8a
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.

4.980 × 10⁹⁴(95-digit number)
49805386860643836530…60789805512725824539
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
4.980 × 10⁹⁴(95-digit number)
49805386860643836530…60789805512725824539
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.961 × 10⁹⁴(95-digit number)
99610773721287673060…21579611025451649079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.992 × 10⁹⁵(96-digit number)
19922154744257534612…43159222050903298159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.984 × 10⁹⁵(96-digit number)
39844309488515069224…86318444101806596319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.968 × 10⁹⁵(96-digit number)
79688618977030138448…72636888203613192639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.593 × 10⁹⁶(97-digit number)
15937723795406027689…45273776407226385279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.187 × 10⁹⁶(97-digit number)
31875447590812055379…90547552814452770559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.375 × 10⁹⁶(97-digit number)
63750895181624110758…81095105628905541119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.275 × 10⁹⁷(98-digit number)
12750179036324822151…62190211257811082239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.550 × 10⁹⁷(98-digit number)
25500358072649644303…24380422515622164479
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:57,692,970 XPM·at block #6,806,111 · updates every 60s
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