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Block #831,655

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/28/2014, 7:51:15 AM Β· Difficulty 10.9789 Β· 5,975,696 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
86ac268a12b3ecb003fd30ef4a16b37ecb75794c00597edb01f6d80ea6421c34
View on Chainz β†—

Height

#831,655

Difficulty

10.978917

Transactions

2

Size

425 B

Version

2

Bits

0afa9a4d

Nonce

80,694,312

Timestamp

11/28/2014, 7:51:15 AM

Confirmations

5,975,696

Mined by

⛏️ P2SHAaeok7672uULAaNu5vSg96VTC816cP8vog

Merkle Root

0f061e37a230ae4aac8e954dcf3f0130bae1714921a36dacbb6f9b35584e74a6
Transactions (2)
Coinbase2d4b088afe46cd…0bdd9d9d45abb6
1 in β†’ 1 out8.2900 XPM109 B
Aaeok767…16cP8vog
2302cba9074387…7a25d76c15e4d5
1 in β†’ 2 out25441.0056 XPM226 B
ASUDdu12…YS6UsfsUAJpyvxe8…GTa6v9G3
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.

2.488 Γ— 10⁹⁴(95-digit number)
24886277620559420985…40809875467178790639
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
2.488 Γ— 10⁹⁴(95-digit number)
24886277620559420985…40809875467178790639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.977 Γ— 10⁹⁴(95-digit number)
49772555241118841970…81619750934357581279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.954 Γ— 10⁹⁴(95-digit number)
99545110482237683941…63239501868715162559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.990 Γ— 10⁹⁡(96-digit number)
19909022096447536788…26479003737430325119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.981 Γ— 10⁹⁡(96-digit number)
39818044192895073576…52958007474860650239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.963 Γ— 10⁹⁡(96-digit number)
79636088385790147153…05916014949721300479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.592 Γ— 10⁹⁢(97-digit number)
15927217677158029430…11832029899442600959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.185 Γ— 10⁹⁢(97-digit number)
31854435354316058861…23664059798885201919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.370 Γ— 10⁹⁢(97-digit number)
63708870708632117722…47328119597770403839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.274 Γ— 10⁹⁷(98-digit number)
12741774141726423544…94656239195540807679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.548 Γ— 10⁹⁷(98-digit number)
25483548283452847089…89312478391081615359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,702,829 XPMΒ·at block #6,807,350 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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