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Block #1,831,719

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/1/2016, 4:07:16 PM Β· Difficulty 10.7254 Β· 5,007,778 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bca811cd19514d06aa052e61da497fd09bf652d67f5fcb0d7d8fa5f9a26e6809
View on Chainz β†—

Height

#1,831,719

Difficulty

10.725402

Transactions

1

Size

200 B

Version

2

Bits

0ab9b3f4

Nonce

1,967,017,627

Timestamp

11/1/2016, 4:07:16 PM

Confirmations

5,007,778

Mined by

⛏️ P2SHAJoVY8qGP3bYWthVyHvFupFfhMsMBv7ZsW

Merkle Root

d1e295e174a630e1598247413d1ddc974e061c483ad4f60ce5a0442eaef410f3
Transactions (1)
Coinbased1e295e174a630…a0442eaef410f3
1 in β†’ 1 out8.6800 XPM110 B
AJoVY8qG…sMBv7ZsW
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.

2.609 Γ— 10⁹⁴(95-digit number)
26098621075216046673…63496793210629810399
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
2.609 Γ— 10⁹⁴(95-digit number)
26098621075216046673…63496793210629810399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.219 Γ— 10⁹⁴(95-digit number)
52197242150432093347…26993586421259620799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.043 Γ— 10⁹⁡(96-digit number)
10439448430086418669…53987172842519241599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.087 Γ— 10⁹⁡(96-digit number)
20878896860172837338…07974345685038483199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.175 Γ— 10⁹⁡(96-digit number)
41757793720345674677…15948691370076966399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.351 Γ— 10⁹⁡(96-digit number)
83515587440691349355…31897382740153932799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.670 Γ— 10⁹⁢(97-digit number)
16703117488138269871…63794765480307865599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.340 Γ— 10⁹⁢(97-digit number)
33406234976276539742…27589530960615731199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.681 Γ— 10⁹⁢(97-digit number)
66812469952553079484…55179061921231462399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.336 Γ— 10⁹⁷(98-digit number)
13362493990510615896…10358123842462924799
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:57,960,272 XPMΒ·at block #6,839,496 Β· updates every 60s
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