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Block #1,612,364

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/3/2016, 12:46:26 PM Β· Difficulty 10.6021 Β· 5,228,715 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e5731c287f736a467a4cb69bd343c3fc31b745cbf66c1171f8c0f29231e0fc1
View on Chainz β†—

Height

#1,612,364

Difficulty

10.602140

Transactions

1

Size

199 B

Version

2

Bits

0a9a25da

Nonce

455,640,501

Timestamp

6/3/2016, 12:46:26 PM

Confirmations

5,228,715

Mined by

⛏️ P2SHAGEjTDgnSAQEWXX6WSZ8d8saG3TjmzqFLC

Merkle Root

767799205c80dbf7a86211ef04fe59fa1ef4eb42c486001fc5148a68e3f3848f
Transactions (1)
Coinbase767799205c80db…148a68e3f3848f
1 in β†’ 1 out8.8800 XPM109 B
AGEjTDgn…TjmzqFLC
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.

6.917 Γ— 10⁹³(94-digit number)
69172006159285959710…24068654789310981869
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
6.917 Γ— 10⁹³(94-digit number)
69172006159285959710…24068654789310981869
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.383 Γ— 10⁹⁴(95-digit number)
13834401231857191942…48137309578621963739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.766 Γ— 10⁹⁴(95-digit number)
27668802463714383884…96274619157243927479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.533 Γ— 10⁹⁴(95-digit number)
55337604927428767768…92549238314487854959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.106 Γ— 10⁹⁡(96-digit number)
11067520985485753553…85098476628975709919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.213 Γ— 10⁹⁡(96-digit number)
22135041970971507107…70196953257951419839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.427 Γ— 10⁹⁡(96-digit number)
44270083941943014215…40393906515902839679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.854 Γ— 10⁹⁡(96-digit number)
88540167883886028430…80787813031805679359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.770 Γ— 10⁹⁢(97-digit number)
17708033576777205686…61575626063611358719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.541 Γ— 10⁹⁢(97-digit number)
35416067153554411372…23151252127222717439
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:57,972,995 XPMΒ·at block #6,841,078 Β· updates every 60s
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