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Block #2,122,393

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/18/2017, 2:25:49 PM Β· Difficulty 10.9156 Β· 4,722,164 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0b8f7c07d4162bd8c1c32d5e3083bcf27bd5a977b4ab58b8d38af83b43e982c6
View on Chainz β†—

Height

#2,122,393

Difficulty

10.915573

Transactions

1

Size

200 B

Version

2

Bits

0aea62fa

Nonce

270,568,791

Timestamp

5/18/2017, 2:25:49 PM

Confirmations

4,722,164

Mined by

⛏️ P2SHAUbhhSELb73GFwAcXacpY1mCm8FPRuAZzJ

Merkle Root

88cdc43d6d22a39716ecadfbd5f24918fe766b235b0edfcd8652c6bfe4c375cf
Transactions (1)
Coinbase88cdc43d6d22a3…52c6bfe4c375cf
1 in β†’ 1 out8.3800 XPM109 B
AUbhhSEL…FPRuAZzJ
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.

1.890 Γ— 10⁹⁷(98-digit number)
18901111184678842092…04931826846507059199
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
1.890 Γ— 10⁹⁷(98-digit number)
18901111184678842092…04931826846507059199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.780 Γ— 10⁹⁷(98-digit number)
37802222369357684184…09863653693014118399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.560 Γ— 10⁹⁷(98-digit number)
75604444738715368369…19727307386028236799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.512 Γ— 10⁹⁸(99-digit number)
15120888947743073673…39454614772056473599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.024 Γ— 10⁹⁸(99-digit number)
30241777895486147347…78909229544112947199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.048 Γ— 10⁹⁸(99-digit number)
60483555790972294695…57818459088225894399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.209 Γ— 10⁹⁹(100-digit number)
12096711158194458939…15636918176451788799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.419 Γ— 10⁹⁹(100-digit number)
24193422316388917878…31273836352903577599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.838 Γ— 10⁹⁹(100-digit number)
48386844632777835756…62547672705807155199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.677 Γ— 10⁹⁹(100-digit number)
96773689265555671513…25095345411614310399
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:58,000,859 XPMΒ·at block #6,844,556 Β· updates every 60s
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