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Block #1,534,608

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/10/2016, 8:44:23 AM Β· Difficulty 10.6176 Β· 5,292,584 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e11ea7c07c17bb04534808ca66a44b9518f4e8d11ac69d52c34821a7a922a3df
View on Chainz β†—

Height

#1,534,608

Difficulty

10.617564

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e18b5

Nonce

1,111,648,319

Timestamp

4/10/2016, 8:44:23 AM

Confirmations

5,292,584

Mined by

⛏️ P2SHARvWt2SmgVYRj1dX3zWAvnEAyFBLbcfN8D

Merkle Root

8d474c3cf8f94e6b7d48a1cc320e0f413912350443c95f259256611622fb4f86
Transactions (2)
Coinbasee8929d4fd0f59a…3d836ccd93bc3a
1 in β†’ 1 out8.9400 XPM109 B
ARvWt2Sm…BLbcfN8D
303940a7ce7a8f…43897525ef4843
51 in β†’ 1 out1242.2885 XPM7.42 KB
AWXJw6oi…1b9URKWc
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.

3.508 Γ— 10⁹⁴(95-digit number)
35080070821887110752…15113566432590998399
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
3.508 Γ— 10⁹⁴(95-digit number)
35080070821887110752…15113566432590998399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.016 Γ— 10⁹⁴(95-digit number)
70160141643774221505…30227132865181996799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.403 Γ— 10⁹⁡(96-digit number)
14032028328754844301…60454265730363993599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.806 Γ— 10⁹⁡(96-digit number)
28064056657509688602…20908531460727987199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.612 Γ— 10⁹⁡(96-digit number)
56128113315019377204…41817062921455974399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.122 Γ— 10⁹⁢(97-digit number)
11225622663003875440…83634125842911948799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.245 Γ— 10⁹⁢(97-digit number)
22451245326007750881…67268251685823897599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.490 Γ— 10⁹⁢(97-digit number)
44902490652015501763…34536503371647795199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.980 Γ— 10⁹⁢(97-digit number)
89804981304031003526…69073006743295590399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.796 Γ— 10⁹⁷(98-digit number)
17960996260806200705…38146013486591180799
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:57,861,631 XPMΒ·at block #6,827,191 Β· updates every 60s
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