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Block #1,534,736

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/10/2016, 10:46:22 AM Β· Difficulty 10.6181 Β· 5,282,361 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c31135c7afc33b411938664e5ebb4cc20aadc296c08a259b059998da648d5700
View on Chainz β†—

Height

#1,534,736

Difficulty

10.618122

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e3d3e

Nonce

1,141,092,854

Timestamp

4/10/2016, 10:46:22 AM

Confirmations

5,282,361

Mined by

⛏️ P2SHAH5wUV7pWctm9qpqJaCrcTDU4YcUCMSK6v

Merkle Root

e4d23965c8596b97cb78dea8a076760114ea4685a8a0617418f2669982a2be19
Transactions (2)
Coinbase7c184ee731b938…d3e45ba59de124
1 in β†’ 1 out8.9400 XPM110 B
AH5wUV7p…cUCMSK6v
71e63039661cef…aa4102f8855855
51 in β†’ 1 out3117.1377 XPM7.42 KB
Aa6ULL8j…5QCuMCv5
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.

3.154 Γ— 10⁹⁴(95-digit number)
31548411357495000252…91849032954553229819
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
3.154 Γ— 10⁹⁴(95-digit number)
31548411357495000252…91849032954553229819
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.309 Γ— 10⁹⁴(95-digit number)
63096822714990000504…83698065909106459639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.261 Γ— 10⁹⁡(96-digit number)
12619364542998000100…67396131818212919279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.523 Γ— 10⁹⁡(96-digit number)
25238729085996000201…34792263636425838559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.047 Γ— 10⁹⁡(96-digit number)
50477458171992000403…69584527272851677119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.009 Γ— 10⁹⁢(97-digit number)
10095491634398400080…39169054545703354239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.019 Γ— 10⁹⁢(97-digit number)
20190983268796800161…78338109091406708479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.038 Γ— 10⁹⁢(97-digit number)
40381966537593600323…56676218182813416959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.076 Γ— 10⁹⁢(97-digit number)
80763933075187200646…13352436365626833919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.615 Γ— 10⁹⁷(98-digit number)
16152786615037440129…26704872731253667839
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:57,780,813 XPMΒ·at block #6,817,096 Β· updates every 60s
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