Block #1,410,754

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/12/2016, 10:29:40 PM · Difficulty 10.8048 · 5,430,668 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
16463df57b605d2f7b2d58bb192981708e6f19367d1147ce447e0bbfc9883788

Height

#1,410,754

Difficulty

10.804833

Transactions

2

Size

2.04 KB

Version

2

Bits

0ace0985

Nonce

298,072,314

Timestamp

1/12/2016, 10:29:40 PM

Confirmations

5,430,668

Merkle Root

460a0fc68731ac52132dce56756f4b5d3e19c2379fd61959e24f16340a6ca8ae
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.

9.964 × 10⁹¹(92-digit number)
99646824700913471003…20674782317738712561
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
9.964 × 10⁹¹(92-digit number)
99646824700913471003…20674782317738712561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.992 × 10⁹²(93-digit number)
19929364940182694200…41349564635477425121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.985 × 10⁹²(93-digit number)
39858729880365388401…82699129270954850241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.971 × 10⁹²(93-digit number)
79717459760730776803…65398258541909700481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.594 × 10⁹³(94-digit number)
15943491952146155360…30796517083819400961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.188 × 10⁹³(94-digit number)
31886983904292310721…61593034167638801921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.377 × 10⁹³(94-digit number)
63773967808584621442…23186068335277603841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.275 × 10⁹⁴(95-digit number)
12754793561716924288…46372136670555207681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.550 × 10⁹⁴(95-digit number)
25509587123433848576…92744273341110415361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.101 × 10⁹⁴(95-digit number)
51019174246867697153…85488546682220830721
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:57,975,752 XPM·at block #6,841,421 · updates every 60s
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