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Block #31,016

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 9:40:42 PM Β· Difficulty 7.9879 Β· 6,778,640 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e27148cc8164e3e654ce6f6ee79c766b1ccb83cad310c6afbb146682660e5506
View on Chainz β†—

Height

#31,016

Difficulty

7.987945

Transactions

1

Size

200 B

Version

2

Bits

07fce9fc

Nonce

113

Timestamp

7/13/2013, 9:40:42 PM

Confirmations

6,778,640

Mined by

⛏️ P2SHAV6P7enUMtWL6sjxBf1aCsLJbsVLHeixvR

Merkle Root

f486e1ec7482d009660e5dc6c9b3ca9b0cd59e73c965d48cb0cb2e3b1d8c2b02
Transactions (1)
Coinbasef486e1ec7482d0…cb2e3b1d8c2b02
1 in β†’ 1 out15.6500 XPM109 B
AV6P7enU…VLHeixvR
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.

5.563 Γ— 10⁹⁢(97-digit number)
55630462885973078496…15451239391190630999
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
5.563 Γ— 10⁹⁢(97-digit number)
55630462885973078496…15451239391190630999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.112 Γ— 10⁹⁷(98-digit number)
11126092577194615699…30902478782381261999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.225 Γ— 10⁹⁷(98-digit number)
22252185154389231398…61804957564762523999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.450 Γ— 10⁹⁷(98-digit number)
44504370308778462797…23609915129525047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.900 Γ— 10⁹⁷(98-digit number)
89008740617556925594…47219830259050095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.780 Γ— 10⁹⁸(99-digit number)
17801748123511385118…94439660518100191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.560 Γ— 10⁹⁸(99-digit number)
35603496247022770237…88879321036200383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.120 Γ— 10⁹⁸(99-digit number)
71206992494045540475…77758642072400767999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,721,330 XPMΒ·at block #6,809,655 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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