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Block #1,712,226

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/11/2016, 1:10:50 PM Β· Difficulty 10.6426 Β· 5,127,687 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4a9e6f1bf4b6d4f1da5dff71b77f25056a415adf4e00b7ddd53330eab52a2071
View on Chainz β†—

Height

#1,712,226

Difficulty

10.642576

Transactions

1

Size

243 B

Version

2

Bits

0aa47fd7

Nonce

170,128,865

Timestamp

8/11/2016, 1:10:50 PM

Confirmations

5,127,687

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

d1a1505e2d02088985397ee47a0f1c5ba9af7a64bd654246e47de529283a89e2
Transactions (1)
Coinbased1a1505e2d0208…7de529283a89e2
1 in β†’ 2 out8.8200 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

3.876 Γ— 10⁹⁢(97-digit number)
38765213447910744971…45256210742316835359
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
3.876 Γ— 10⁹⁢(97-digit number)
38765213447910744971…45256210742316835359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.753 Γ— 10⁹⁢(97-digit number)
77530426895821489942…90512421484633670719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.550 Γ— 10⁹⁷(98-digit number)
15506085379164297988…81024842969267341439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.101 Γ— 10⁹⁷(98-digit number)
31012170758328595976…62049685938534682879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.202 Γ— 10⁹⁷(98-digit number)
62024341516657191953…24099371877069365759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.240 Γ— 10⁹⁸(99-digit number)
12404868303331438390…48198743754138731519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.480 Γ— 10⁹⁸(99-digit number)
24809736606662876781…96397487508277463039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.961 Γ— 10⁹⁸(99-digit number)
49619473213325753562…92794975016554926079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.923 Γ— 10⁹⁸(99-digit number)
99238946426651507125…85589950033109852159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.984 Γ— 10⁹⁹(100-digit number)
19847789285330301425…71179900066219704319
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:57,963,604 XPMΒ·at block #6,839,912 Β· updates every 60s
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