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Block #2,059,897

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/7/2017, 3:39:17 AM Β· Difficulty 10.8502 Β· 4,773,375 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d6f56b85b8d97024493a4765123c8645b7166ae0b4d94a875d6cc8cd7cc97880
View on Chainz β†—

Height

#2,059,897

Difficulty

10.850180

Transactions

1

Size

209 B

Version

2

Bits

0ad9a55f

Nonce

17,533,863

Timestamp

4/7/2017, 3:39:17 AM

Confirmations

4,773,375

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

4fad626c43be5fd217a4493cbc28edd88e8a6ea6e32735812d3f1a47e81bba1e
Transactions (1)
Coinbase4fad626c43be5f…3f1a47e81bba1e
1 in β†’ 1 out8.4800 XPM118 B
AM6GYpjw…aw86QDtR
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.

6.518 Γ— 10⁹⁢(97-digit number)
65187947563115943558…94006821371960649599
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
6.518 Γ— 10⁹⁢(97-digit number)
65187947563115943558…94006821371960649599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.303 Γ— 10⁹⁷(98-digit number)
13037589512623188711…88013642743921299199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.607 Γ— 10⁹⁷(98-digit number)
26075179025246377423…76027285487842598399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.215 Γ— 10⁹⁷(98-digit number)
52150358050492754846…52054570975685196799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.043 Γ— 10⁹⁸(99-digit number)
10430071610098550969…04109141951370393599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.086 Γ— 10⁹⁸(99-digit number)
20860143220197101938…08218283902740787199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.172 Γ— 10⁹⁸(99-digit number)
41720286440394203877…16436567805481574399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.344 Γ— 10⁹⁸(99-digit number)
83440572880788407754…32873135610963148799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.668 Γ— 10⁹⁹(100-digit number)
16688114576157681550…65746271221926297599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.337 Γ— 10⁹⁹(100-digit number)
33376229152315363101…31492542443852595199
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:57,910,370 XPMΒ·at block #6,833,271 Β· updates every 60s
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