Block #1,600,207

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/26/2016, 2:04:21 AM · Difficulty 10.6021 · 5,227,196 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5f9f2076c5923a6f2edc2994c2368bb8522490c6b31e7f61c2dc49bdb93e34b8

Height

#1,600,207

Difficulty

10.602055

Transactions

2

Size

1.15 KB

Version

2

Bits

0a9a204a

Nonce

1,094,961,698

Timestamp

5/26/2016, 2:04:21 AM

Confirmations

5,227,196

Merkle Root

8c962a0e2a2d52c4737ab6b05ea7d847a461c3ebcaafb49f1e151873accb5679
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.

8.327 × 10⁹⁴(95-digit number)
83278461829020727922…42791430529442552319
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
8.327 × 10⁹⁴(95-digit number)
83278461829020727922…42791430529442552319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.665 × 10⁹⁵(96-digit number)
16655692365804145584…85582861058885104639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.331 × 10⁹⁵(96-digit number)
33311384731608291169…71165722117770209279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.662 × 10⁹⁵(96-digit number)
66622769463216582338…42331444235540418559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.332 × 10⁹⁶(97-digit number)
13324553892643316467…84662888471080837119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.664 × 10⁹⁶(97-digit number)
26649107785286632935…69325776942161674239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.329 × 10⁹⁶(97-digit number)
53298215570573265870…38651553884323348479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.065 × 10⁹⁷(98-digit number)
10659643114114653174…77303107768646696959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.131 × 10⁹⁷(98-digit number)
21319286228229306348…54606215537293393919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.263 × 10⁹⁷(98-digit number)
42638572456458612696…09212431074586787839
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:57,863,329 XPM·at block #6,827,402 · updates every 60s
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