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Block #1,020,453

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/17/2015, 10:59:24 AM Β· Difficulty 10.7490 Β· 5,788,925 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a7db525c86c4fbec27a7b96ec317ca7c584a8ab7f265507a03f3aa2ed5c28ce6
View on Chainz β†—

Height

#1,020,453

Difficulty

10.749037

Transactions

2

Size

390 B

Version

2

Bits

0abfc0e2

Nonce

417,012,042

Timestamp

4/17/2015, 10:59:24 AM

Confirmations

5,788,925

Mined by

⛏️ P2SHAVH5fn28AmQ74o51SvN5cLXbCEv9eLP6ai

Merkle Root

b77cac1cb322f1b1769f34b2d746458462925adc0200b852bd5218aa86f86e72
Transactions (2)
Coinbasebd8f0722b97952…2a7ad0a5c6a8cb
1 in β†’ 1 out8.6500 XPM109 B
AVH5fn28…v9eLP6ai
9d3590c211bfc1…36efb5db2d01a1
1 in β†’ 1 out0.0913 XPM192 B
AXv9HTzf…dfNPqFw8
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.

1.877 Γ— 10⁹²(93-digit number)
18775880167144276244…22575416674596602641
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.877 Γ— 10⁹²(93-digit number)
18775880167144276244…22575416674596602641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.755 Γ— 10⁹²(93-digit number)
37551760334288552489…45150833349193205281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.510 Γ— 10⁹²(93-digit number)
75103520668577104978…90301666698386410561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.502 Γ— 10⁹³(94-digit number)
15020704133715420995…80603333396772821121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.004 Γ— 10⁹³(94-digit number)
30041408267430841991…61206666793545642241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.008 Γ— 10⁹³(94-digit number)
60082816534861683982…22413333587091284481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.201 Γ— 10⁹⁴(95-digit number)
12016563306972336796…44826667174182568961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.403 Γ— 10⁹⁴(95-digit number)
24033126613944673592…89653334348365137921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.806 Γ— 10⁹⁴(95-digit number)
48066253227889347185…79306668696730275841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.613 Γ— 10⁹⁴(95-digit number)
96132506455778694371…58613337393460551681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.922 Γ— 10⁹⁡(96-digit number)
19226501291155738874…17226674786921103361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,719,094 XPMΒ·at block #6,809,377 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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