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Block #1,285,875

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/17/2015, 7:46:23 AM Β· Difficulty 10.8447 Β· 5,539,186 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a1bc4c3d46958eced31fb347ad09416ad07ef3b85149a50c5d5654f4ea3dbf9a
View on Chainz β†—

Height

#1,285,875

Difficulty

10.844652

Transactions

2

Size

4.76 KB

Version

2

Bits

0ad83b1d

Nonce

935,138,970

Timestamp

10/17/2015, 7:46:23 AM

Confirmations

5,539,186

Mined by

⛏️ P2SHAYtsY43pFtYj9zXuSE9S7FKcmg7CrsFe4G

Merkle Root

5ecb59c27463f18dddde7e672e139da43d651a2e402fac223943414cc1b4e273
Transactions (2)
Coinbase8b6a039ac57957…00e2419d2844c0
1 in β†’ 1 out8.5700 XPM110 B
AYtsY43p…7CrsFe4G
7659511572cea4…a7a9fa5a242828
31 in β†’ 2 out825.7684 XPM4.56 KB
AToAueMA…4RqkxgfNANLKwi9R…VqgWbRWq
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.

1.363 Γ— 10⁹⁴(95-digit number)
13632456684542516799…77352998264176528599
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
1.363 Γ— 10⁹⁴(95-digit number)
13632456684542516799…77352998264176528599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.726 Γ— 10⁹⁴(95-digit number)
27264913369085033599…54705996528353057199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.452 Γ— 10⁹⁴(95-digit number)
54529826738170067199…09411993056706114399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.090 Γ— 10⁹⁡(96-digit number)
10905965347634013439…18823986113412228799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.181 Γ— 10⁹⁡(96-digit number)
21811930695268026879…37647972226824457599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.362 Γ— 10⁹⁡(96-digit number)
43623861390536053759…75295944453648915199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.724 Γ— 10⁹⁡(96-digit number)
87247722781072107519…50591888907297830399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.744 Γ— 10⁹⁢(97-digit number)
17449544556214421503…01183777814595660799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.489 Γ— 10⁹⁢(97-digit number)
34899089112428843007…02367555629191321599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.979 Γ— 10⁹⁢(97-digit number)
69798178224857686015…04735111258382643199
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:57,844,574 XPMΒ·at block #6,825,060 Β· updates every 60s
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