Block #2,456,485

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/4/2018, 12:43:42 AM · Difficulty 10.9535 · 4,384,936 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f1d735dabb472f848f9b3a651a6851f068855a42f428a2e0ba252d4fdaf27ae9

Height

#2,456,485

Difficulty

10.953544

Transactions

59

Size

21.65 KB

Version

2

Bits

0af41b6f

Nonce

1,283,183,894

Timestamp

1/4/2018, 12:43:42 AM

Confirmations

4,384,936

Merkle Root

4f48e29b0e5375da0583956c7d6136ac3cbc8abf918aa3bbf4697d25c7a66730
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.

4.987 × 10⁹⁴(95-digit number)
49876438414912766394…28782785335168880641
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
4.987 × 10⁹⁴(95-digit number)
49876438414912766394…28782785335168880641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.975 × 10⁹⁴(95-digit number)
99752876829825532789…57565570670337761281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.995 × 10⁹⁵(96-digit number)
19950575365965106557…15131141340675522561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.990 × 10⁹⁵(96-digit number)
39901150731930213115…30262282681351045121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.980 × 10⁹⁵(96-digit number)
79802301463860426231…60524565362702090241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.596 × 10⁹⁶(97-digit number)
15960460292772085246…21049130725404180481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.192 × 10⁹⁶(97-digit number)
31920920585544170492…42098261450808360961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.384 × 10⁹⁶(97-digit number)
63841841171088340985…84196522901616721921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.276 × 10⁹⁷(98-digit number)
12768368234217668197…68393045803233443841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.553 × 10⁹⁷(98-digit number)
25536736468435336394…36786091606466887681
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,975,744 XPM·at block #6,841,420 · updates every 60s
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