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Block #31,139

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 10:10:13 PM Β· Difficulty 7.9882 Β· 6,786,863 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
85de077ed569030a180ae0617f75dc283768768dc72a4619d175310bd970b3e7
View on Chainz β†—

Height

#31,139

Difficulty

7.988170

Transactions

1

Size

198 B

Version

2

Bits

07fcf8b2

Nonce

130

Timestamp

7/13/2013, 10:10:13 PM

Confirmations

6,786,863

Mined by

⛏️ P2SHAJbz55M2Xd4eSVXFrry1sb6y1EmoHxsz79

Merkle Root

4c5a5796d3d85b85b5d0a8be0671fa2f2508cd1647e9432134041c2ed6a25fb4
Transactions (1)
Coinbase4c5a5796d3d85b…041c2ed6a25fb4
1 in β†’ 1 out15.6500 XPM109 B
AJbz55M2…moHxsz79
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.

1.254 Γ— 10⁹³(94-digit number)
12545409279491274034…96062167795123775899
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
1.254 Γ— 10⁹³(94-digit number)
12545409279491274034…96062167795123775899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.509 Γ— 10⁹³(94-digit number)
25090818558982548069…92124335590247551799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.018 Γ— 10⁹³(94-digit number)
50181637117965096138…84248671180495103599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.003 Γ— 10⁹⁴(95-digit number)
10036327423593019227…68497342360990207199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.007 Γ— 10⁹⁴(95-digit number)
20072654847186038455…36994684721980414399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.014 Γ— 10⁹⁴(95-digit number)
40145309694372076910…73989369443960828799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.029 Γ— 10⁹⁴(95-digit number)
80290619388744153821…47978738887921657599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.605 Γ— 10⁹⁡(96-digit number)
16058123877748830764…95957477775843315199
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:57,788,081 XPMΒ·at block #6,818,001 Β· updates every 60s
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