Block #1,371,984

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/16/2015, 9:30:43 PM · Difficulty 10.8100 · 5,437,674 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5bbebf8695470f80f139b897a37bcd2a6c34379fceb98aef5530bcb710a6ffe9

Height

#1,371,984

Difficulty

10.810029

Transactions

4

Size

5.22 KB

Version

2

Bits

0acf5e15

Nonce

1,915,171,955

Timestamp

12/16/2015, 9:30:43 PM

Confirmations

5,437,674

Merkle Root

208d44fe8cb003ecd5785f69f91d54c80838733e933cd28ddc92c8ae997a9bec
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.

6.262 × 10⁹³(94-digit number)
62620978696580298364…42937560235283646239
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
6.262 × 10⁹³(94-digit number)
62620978696580298364…42937560235283646239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.252 × 10⁹⁴(95-digit number)
12524195739316059672…85875120470567292479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.504 × 10⁹⁴(95-digit number)
25048391478632119345…71750240941134584959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.009 × 10⁹⁴(95-digit number)
50096782957264238691…43500481882269169919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.001 × 10⁹⁵(96-digit number)
10019356591452847738…87000963764538339839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.003 × 10⁹⁵(96-digit number)
20038713182905695476…74001927529076679679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.007 × 10⁹⁵(96-digit number)
40077426365811390953…48003855058153359359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.015 × 10⁹⁵(96-digit number)
80154852731622781906…96007710116306718719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.603 × 10⁹⁶(97-digit number)
16030970546324556381…92015420232613437439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.206 × 10⁹⁶(97-digit number)
32061941092649112762…84030840465226874879
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:57,721,337 XPM·at block #6,809,657 · updates every 60s
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