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Block #1,534,504

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/10/2016, 7:10:16 AM Β· Difficulty 10.6167 Β· 5,278,543 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
76e40ad5b30aa4124c0a3903657d91bf0a8bc561924e77e4a55b1f74675541bc
View on Chainz β†—

Height

#1,534,504

Difficulty

10.616674

Transactions

2

Size

7.60 KB

Version

2

Bits

0a9dde58

Nonce

192,319,009

Timestamp

4/10/2016, 7:10:16 AM

Confirmations

5,278,543

Mined by

⛏️ P2SHAHdXXkSEe1xY31bkr4V6DW4oWStki9pz3r

Merkle Root

8dada51f23013dbb671b4b6350dac59b06be154a52546865dd77a4ba9f562370
Transactions (2)
Coinbasec202b9919cdc93…341a8bd0a14c95
1 in β†’ 1 out8.9400 XPM109 B
AHdXXkSE…tki9pz3r
914af06b17b9e2…69bc528ccac7bd
51 in β†’ 1 out2764.9452 XPM7.41 KB
ALx7KBfL…WwN2rHKU
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.

2.833 Γ— 10⁹⁴(95-digit number)
28335924974900220952…99766725435428846799
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
2.833 Γ— 10⁹⁴(95-digit number)
28335924974900220952…99766725435428846799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.667 Γ— 10⁹⁴(95-digit number)
56671849949800441904…99533450870857693599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.133 Γ— 10⁹⁡(96-digit number)
11334369989960088380…99066901741715387199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.266 Γ— 10⁹⁡(96-digit number)
22668739979920176761…98133803483430774399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.533 Γ— 10⁹⁡(96-digit number)
45337479959840353523…96267606966861548799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.067 Γ— 10⁹⁡(96-digit number)
90674959919680707047…92535213933723097599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.813 Γ— 10⁹⁢(97-digit number)
18134991983936141409…85070427867446195199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.626 Γ— 10⁹⁢(97-digit number)
36269983967872282818…70140855734892390399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.253 Γ— 10⁹⁢(97-digit number)
72539967935744565637…40281711469784780799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.450 Γ— 10⁹⁷(98-digit number)
14507993587148913127…80563422939569561599
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:57,748,421 XPMΒ·at block #6,813,046 Β· updates every 60s
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