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Block #1,752,275

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/7/2016, 8:25:57 PM Β· Difficulty 10.6926 Β· 5,060,471 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
54881b16695e97895dcd045fc29a46f61d0684bfac98412728440df44799de88
View on Chainz β†—

Height

#1,752,275

Difficulty

10.692612

Transactions

1

Size

199 B

Version

2

Bits

0ab14eff

Nonce

159,946

Timestamp

9/7/2016, 8:25:57 PM

Confirmations

5,060,471

Mined by

⛏️ P2SHARaPyHgjo2zpePAfC2xk8aeQGMnA9veLYH

Merkle Root

251192fcd38d94dee6d77a9a20f881c0cf0509a54d7c899948a0cbd327b4d0f1
Transactions (1)
Coinbase251192fcd38d94…a0cbd327b4d0f1
1 in β†’ 1 out8.7300 XPM109 B
ARaPyHgj…nA9veLYH
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.

4.717 Γ— 10⁹⁡(96-digit number)
47172346844061817174…61310198392959999999
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
4.717 Γ— 10⁹⁡(96-digit number)
47172346844061817174…61310198392959999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.434 Γ— 10⁹⁡(96-digit number)
94344693688123634348…22620396785919999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.886 Γ— 10⁹⁢(97-digit number)
18868938737624726869…45240793571839999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.773 Γ— 10⁹⁢(97-digit number)
37737877475249453739…90481587143679999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.547 Γ— 10⁹⁢(97-digit number)
75475754950498907478…80963174287359999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.509 Γ— 10⁹⁷(98-digit number)
15095150990099781495…61926348574719999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.019 Γ— 10⁹⁷(98-digit number)
30190301980199562991…23852697149439999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.038 Γ— 10⁹⁷(98-digit number)
60380603960399125983…47705394298879999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.207 Γ— 10⁹⁸(99-digit number)
12076120792079825196…95410788597759999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.415 Γ— 10⁹⁸(99-digit number)
24152241584159650393…90821577195519999999
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:57,746,011 XPMΒ·at block #6,812,745 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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