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Block #1,734,050

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/25/2016, 9:04:51 PM Β· Difficulty 10.7186 Β· 5,076,075 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
615d322f8628b83a7beccb61a4de37c0e06c475a6172a86587674a13880f7564
View on Chainz β†—

Height

#1,734,050

Difficulty

10.718579

Transactions

2

Size

4.71 KB

Version

2

Bits

0ab7f4cc

Nonce

542,743,188

Timestamp

8/25/2016, 9:04:51 PM

Confirmations

5,076,075

Mined by

⛏️ P2SHAL1ebr5ypc9pSjSrQVyC4cbDL687sEHifY

Merkle Root

235d165f8c9ff7daa10b04ebcfcb20a847bf8c0ef6c01015479acc9092750ae0
Transactions (2)
Coinbase6d02a3274558df…bbbc2539d989ff
1 in β†’ 1 out8.7400 XPM110 B
AL1ebr5y…87sEHifY
3cba8528f81af7…edddbb98497240
31 in β†’ 1 out239.4321 XPM4.52 KB
Acso9ZA6…KzouUva2
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.

4.114 Γ— 10⁹⁴(95-digit number)
41149970843523385542…34034075794502645201
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
4.114 Γ— 10⁹⁴(95-digit number)
41149970843523385542…34034075794502645201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.229 Γ— 10⁹⁴(95-digit number)
82299941687046771084…68068151589005290401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.645 Γ— 10⁹⁡(96-digit number)
16459988337409354216…36136303178010580801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.291 Γ— 10⁹⁡(96-digit number)
32919976674818708433…72272606356021161601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.583 Γ— 10⁹⁡(96-digit number)
65839953349637416867…44545212712042323201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.316 Γ— 10⁹⁢(97-digit number)
13167990669927483373…89090425424084646401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.633 Γ— 10⁹⁢(97-digit number)
26335981339854966747…78180850848169292801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.267 Γ— 10⁹⁢(97-digit number)
52671962679709933494…56361701696338585601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.053 Γ— 10⁹⁷(98-digit number)
10534392535941986698…12723403392677171201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.106 Γ— 10⁹⁷(98-digit number)
21068785071883973397…25446806785354342401
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,725,073 XPMΒ·at block #6,810,124 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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