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Block #2,237,129

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/4/2017, 9:07:51 PM Β· Difficulty 10.9462 Β· 4,605,145 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4482b6a527c4f0ed63eb1c98dad4125dcfc5daa64dd60e3d77afdc03ec0ed888
View on Chainz β†—

Height

#2,237,129

Difficulty

10.946223

Transactions

1

Size

201 B

Version

2

Bits

0af23bb0

Nonce

879,015,302

Timestamp

8/4/2017, 9:07:51 PM

Confirmations

4,605,145

Mined by

⛏️ P2SHAGnd7Xydae2o34UxWLLiAnQjz9hkL43bJS

Merkle Root

5d11041c9cd43d88e78e1f3d1d16cd67c700875e13e6c22e7a31e40c93cd3db1
Transactions (1)
Coinbase5d11041c9cd43d…31e40c93cd3db1
1 in β†’ 1 out8.3300 XPM110 B
AGnd7Xyd…hkL43bJS
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.

4.421 Γ— 10⁹⁢(97-digit number)
44212714723204439890…52829782364491571199
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
4.421 Γ— 10⁹⁢(97-digit number)
44212714723204439890…52829782364491571199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.842 Γ— 10⁹⁢(97-digit number)
88425429446408879781…05659564728983142399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.768 Γ— 10⁹⁷(98-digit number)
17685085889281775956…11319129457966284799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.537 Γ— 10⁹⁷(98-digit number)
35370171778563551912…22638258915932569599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.074 Γ— 10⁹⁷(98-digit number)
70740343557127103824…45276517831865139199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.414 Γ— 10⁹⁸(99-digit number)
14148068711425420764…90553035663730278399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.829 Γ— 10⁹⁸(99-digit number)
28296137422850841529…81106071327460556799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.659 Γ— 10⁹⁸(99-digit number)
56592274845701683059…62212142654921113599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.131 Γ— 10⁹⁹(100-digit number)
11318454969140336611…24424285309842227199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.263 Γ— 10⁹⁹(100-digit number)
22636909938280673223…48848570619684454399
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:57,982,593 XPMΒ·at block #6,842,273 Β· updates every 60s
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