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Block #231,982

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/28/2013, 7:40:19 PM Β· Difficulty 9.9408 Β· 6,586,009 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ee92ba90f3927a651bea2f5f339f1305d65877605ab80aeb7d93e16f3bb7982b
View on Chainz β†—

Height

#231,982

Difficulty

9.940825

Transactions

1

Size

198 B

Version

2

Bits

09f0d9e5

Nonce

124,431

Timestamp

10/28/2013, 7:40:19 PM

Confirmations

6,586,009

Mined by

⛏️ P2SHAbmEPPa6jgy2BhsLedufSPWF78oBzr9BQY

Merkle Root

c30c795f0507572acd06da037fecd613e483e17314d3a3170671b82d8ab39274
Transactions (1)
Coinbasec30c795f050757…71b82d8ab39274
1 in β†’ 1 out10.1000 XPM109 B
AbmEPPa6…oBzr9BQY
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.

2.022 Γ— 10⁹²(93-digit number)
20223667992369771761…61029801865020254399
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
2.022 Γ— 10⁹²(93-digit number)
20223667992369771761…61029801865020254399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.044 Γ— 10⁹²(93-digit number)
40447335984739543522…22059603730040508799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.089 Γ— 10⁹²(93-digit number)
80894671969479087045…44119207460081017599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.617 Γ— 10⁹³(94-digit number)
16178934393895817409…88238414920162035199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.235 Γ— 10⁹³(94-digit number)
32357868787791634818…76476829840324070399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.471 Γ— 10⁹³(94-digit number)
64715737575583269636…52953659680648140799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.294 Γ— 10⁹⁴(95-digit number)
12943147515116653927…05907319361296281599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.588 Γ— 10⁹⁴(95-digit number)
25886295030233307854…11814638722592563199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.177 Γ— 10⁹⁴(95-digit number)
51772590060466615708…23629277445185126399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,788,000 XPMΒ·at block #6,817,990 Β· updates every 60s
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