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Block #1,736,666

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/27/2016, 4:56:41 PM Β· Difficulty 10.7178 Β· 5,089,613 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4dd5c44d67ade63103b8e7345368e88e83a9b9813f1a5c04ab205ff6be66d107
View on Chainz β†—

Height

#1,736,666

Difficulty

10.717811

Transactions

2

Size

392 B

Version

2

Bits

0ab7c279

Nonce

381,564,838

Timestamp

8/27/2016, 4:56:41 PM

Confirmations

5,089,613

Mined by

⛏️ P2SHAMT5GSiBuosufyQHGN1DqK597Y2Cd8Gc8T

Merkle Root

2e5176b9e77ef2b6f1df30f85ea5e1304aba7a9d44fcc6049c2a6d4dbdaa5cd4
Transactions (2)
Coinbase9b3f1c021bee16…2d98e801e539b1
1 in β†’ 1 out8.7000 XPM109 B
AMT5GSiB…2Cd8Gc8T
7e1ae19676a204…b239ecf215c0e6
1 in β†’ 1 out8.2455 XPM193 B
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.

2.047 Γ— 10⁹⁡(96-digit number)
20474320722878615008…90014976226820682401
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
2.047 Γ— 10⁹⁡(96-digit number)
20474320722878615008…90014976226820682401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.094 Γ— 10⁹⁡(96-digit number)
40948641445757230016…80029952453641364801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.189 Γ— 10⁹⁡(96-digit number)
81897282891514460033…60059904907282729601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.637 Γ— 10⁹⁢(97-digit number)
16379456578302892006…20119809814565459201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.275 Γ— 10⁹⁢(97-digit number)
32758913156605784013…40239619629130918401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.551 Γ— 10⁹⁢(97-digit number)
65517826313211568027…80479239258261836801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.310 Γ— 10⁹⁷(98-digit number)
13103565262642313605…60958478516523673601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.620 Γ— 10⁹⁷(98-digit number)
26207130525284627210…21916957033047347201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.241 Γ— 10⁹⁷(98-digit number)
52414261050569254421…43833914066094694401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.048 Γ— 10⁹⁸(99-digit number)
10482852210113850884…87667828132189388801
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:57,854,369 XPMΒ·at block #6,826,278 Β· updates every 60s
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