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Block #1,701,678

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/3/2016, 10:33:01 PM Β· Difficulty 10.6702 Β· 5,143,166 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e0e62ff9c585ec696b9868348225c8d1c63c6ce0c83debd95ef5a1b6c94abc8c
View on Chainz β†—

Height

#1,701,678

Difficulty

10.670164

Transactions

1

Size

199 B

Version

2

Bits

0aab8fdf

Nonce

473,965,370

Timestamp

8/3/2016, 10:33:01 PM

Confirmations

5,143,166

Mined by

⛏️ P2SHAJbE1j59AhrLCqtLMMpdykiYy8kcY43WN8

Merkle Root

56bb5ed6b5a138f33f65597a36e42bc46003c7c3a353b8c806f1e0b9dcf74c1d
Transactions (1)
Coinbase56bb5ed6b5a138…f1e0b9dcf74c1d
1 in β†’ 1 out8.7700 XPM109 B
AJbE1j59…kcY43WN8
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.

1.884 Γ— 10⁹⁴(95-digit number)
18840734060000625253…74505664999522526079
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
1.884 Γ— 10⁹⁴(95-digit number)
18840734060000625253…74505664999522526079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.768 Γ— 10⁹⁴(95-digit number)
37681468120001250507…49011329999045052159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.536 Γ— 10⁹⁴(95-digit number)
75362936240002501015…98022659998090104319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.507 Γ— 10⁹⁡(96-digit number)
15072587248000500203…96045319996180208639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.014 Γ— 10⁹⁡(96-digit number)
30145174496001000406…92090639992360417279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.029 Γ— 10⁹⁡(96-digit number)
60290348992002000812…84181279984720834559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.205 Γ— 10⁹⁢(97-digit number)
12058069798400400162…68362559969441669119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.411 Γ— 10⁹⁢(97-digit number)
24116139596800800324…36725119938883338239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.823 Γ— 10⁹⁢(97-digit number)
48232279193601600649…73450239877766676479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.646 Γ— 10⁹⁢(97-digit number)
96464558387203201299…46900479755533352959
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:58,003,161 XPMΒ·at block #6,844,843 Β· updates every 60s
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