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Block #2,122,392

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/18/2017, 2:24:54 PM Β· Difficulty 10.9156 Β· 4,719,636 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
480af79b832c5f6ae3eba788e6c806f29a8929063fe26edc401b3d9c24db2f3a
View on Chainz β†—

Height

#2,122,392

Difficulty

10.915560

Transactions

1

Size

199 B

Version

2

Bits

0aea622b

Nonce

1,262,043,701

Timestamp

5/18/2017, 2:24:54 PM

Confirmations

4,719,636

Mined by

⛏️ P2SHAGnk3LuaUmXtcwb24rnjkE91r9UYNynt6b

Merkle Root

83eb43597d4043ad6ac4674b7b4f40f760edc8a0ef3e06951e6aa111a69d9014
Transactions (1)
Coinbase83eb43597d4043…6aa111a69d9014
1 in β†’ 1 out8.3800 XPM109 B
AGnk3Lua…UYNynt6b
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.

1.220 Γ— 10⁹⁴(95-digit number)
12206610291980287420…49471035601166411559
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
1.220 Γ— 10⁹⁴(95-digit number)
12206610291980287420…49471035601166411559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.441 Γ— 10⁹⁴(95-digit number)
24413220583960574841…98942071202332823119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.882 Γ— 10⁹⁴(95-digit number)
48826441167921149683…97884142404665646239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.765 Γ— 10⁹⁴(95-digit number)
97652882335842299366…95768284809331292479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.953 Γ— 10⁹⁡(96-digit number)
19530576467168459873…91536569618662584959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.906 Γ— 10⁹⁡(96-digit number)
39061152934336919746…83073139237325169919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.812 Γ— 10⁹⁡(96-digit number)
78122305868673839493…66146278474650339839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.562 Γ— 10⁹⁢(97-digit number)
15624461173734767898…32292556949300679679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.124 Γ— 10⁹⁢(97-digit number)
31248922347469535797…64585113898601359359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.249 Γ— 10⁹⁢(97-digit number)
62497844694939071594…29170227797202718719
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:57,980,610 XPMΒ·at block #6,842,027 Β· updates every 60s
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