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Block #1,654,826

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/30/2016, 10:13:50 PM Β· Difficulty 10.7824 Β· 5,169,743 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d7340cbd642e50d8babd5981c839b4c71ce4059e58329ec51ffb462ad27518fd
View on Chainz β†—

Height

#1,654,826

Difficulty

10.782375

Transactions

2

Size

6.34 KB

Version

2

Bits

0ac849c2

Nonce

662,668,276

Timestamp

6/30/2016, 10:13:50 PM

Confirmations

5,169,743

Mined by

⛏️ P2SHAb5hZUh23CtPzhpzrQUaQW6QduWy4YsrpA

Merkle Root

2455a8b31eecd869dd5b69f8a88dcfb33b85995ae097d3fc341a73f38883c4ff
Transactions (2)
Coinbase40fc3e99c0b8a9…b2058f73045c05
1 in β†’ 1 out8.7200 XPM109 B
Ab5hZUh2…Wy4YsrpA
07d31944a5175f…d1b41e21cc7288
42 in β†’ 2 out8.6664 XPM6.14 KB
APqk2Vys…Sj3gyJAkAV1Rk4gG…E92Pq4az
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.565 Γ— 10⁹⁴(95-digit number)
15656416157032300967…13105355410379352319
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.565 Γ— 10⁹⁴(95-digit number)
15656416157032300967…13105355410379352319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.131 Γ— 10⁹⁴(95-digit number)
31312832314064601935…26210710820758704639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.262 Γ— 10⁹⁴(95-digit number)
62625664628129203870…52421421641517409279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.252 Γ— 10⁹⁡(96-digit number)
12525132925625840774…04842843283034818559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.505 Γ— 10⁹⁡(96-digit number)
25050265851251681548…09685686566069637119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.010 Γ— 10⁹⁡(96-digit number)
50100531702503363096…19371373132139274239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.002 Γ— 10⁹⁢(97-digit number)
10020106340500672619…38742746264278548479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.004 Γ— 10⁹⁢(97-digit number)
20040212681001345238…77485492528557096959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.008 Γ— 10⁹⁢(97-digit number)
40080425362002690477…54970985057114193919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.016 Γ— 10⁹⁢(97-digit number)
80160850724005380954…09941970114228387839
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,840,617 XPMΒ·at block #6,824,568 Β· updates every 60s
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