Block #1,392,299

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/31/2015, 12:55:12 AM · Difficulty 10.8088 · 5,434,814 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fed94987c085c88bb5c39158474de44eee6b01b1da89cb432fcbd2e047e512c5

Height

#1,392,299

Difficulty

10.808846

Transactions

2

Size

868 B

Version

2

Bits

0acf108c

Nonce

308,746,356

Timestamp

12/31/2015, 12:55:12 AM

Confirmations

5,434,814

Merkle Root

68a8658cd36edce84455ba35f43a15214decea127765893052f7d095f4941b1d
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.

5.727 × 10⁹⁴(95-digit number)
57278388780324218690…03154760302640294439
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
5.727 × 10⁹⁴(95-digit number)
57278388780324218690…03154760302640294439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.145 × 10⁹⁵(96-digit number)
11455677756064843738…06309520605280588879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.291 × 10⁹⁵(96-digit number)
22911355512129687476…12619041210561177759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.582 × 10⁹⁵(96-digit number)
45822711024259374952…25238082421122355519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.164 × 10⁹⁵(96-digit number)
91645422048518749904…50476164842244711039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.832 × 10⁹⁶(97-digit number)
18329084409703749980…00952329684489422079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.665 × 10⁹⁶(97-digit number)
36658168819407499961…01904659368978844159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.331 × 10⁹⁶(97-digit number)
73316337638814999923…03809318737957688319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.466 × 10⁹⁷(98-digit number)
14663267527762999984…07618637475915376639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.932 × 10⁹⁷(98-digit number)
29326535055525999969…15237274951830753279
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:57,861,083 XPM·at block #6,827,112 · updates every 60s
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