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Block #3,445,443

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/23/2019, 1:11:56 PM Β· Difficulty 10.9789 Β· 3,368,550 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1c500430821bc3bde97121d707e73d128b22e0fba7a76cb6ce3dbfe8a45801dd
View on Chainz β†—

Height

#3,445,443

Difficulty

10.978895

Transactions

1

Size

200 B

Version

2

Bits

0afa98d8

Nonce

2,038,755,463

Timestamp

11/23/2019, 1:11:56 PM

Confirmations

3,368,550

Mined by

⛏️ P2SHARvZEYK77gZBh9y1yKkkgZfB7sbZ6zRpvK

Merkle Root

11ebfc6796d053578596e38f728f684f55d39b5ad637574843e620e647a037f4
Transactions (1)
Coinbase11ebfc6796d053…e620e647a037f4
1 in β†’ 1 out8.2800 XPM109 B
ARvZEYK7…bZ6zRpvK
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.

1.969 Γ— 10⁹⁷(98-digit number)
19693013521233631526…66605186435160063999
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
1.969 Γ— 10⁹⁷(98-digit number)
19693013521233631526…66605186435160063999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.938 Γ— 10⁹⁷(98-digit number)
39386027042467263052…33210372870320127999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.877 Γ— 10⁹⁷(98-digit number)
78772054084934526104…66420745740640255999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.575 Γ— 10⁹⁸(99-digit number)
15754410816986905220…32841491481280511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.150 Γ— 10⁹⁸(99-digit number)
31508821633973810441…65682982962561023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.301 Γ— 10⁹⁸(99-digit number)
63017643267947620883…31365965925122047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.260 Γ— 10⁹⁹(100-digit number)
12603528653589524176…62731931850244095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.520 Γ— 10⁹⁹(100-digit number)
25207057307179048353…25463863700488191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.041 Γ— 10⁹⁹(100-digit number)
50414114614358096707…50927727400976383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.008 Γ— 10¹⁰⁰(101-digit number)
10082822922871619341…01855454801952767999
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:57,756,024 XPMΒ·at block #6,813,992 Β· updates every 60s
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