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Block #1,534,716

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 10:28:19 AM Β· Difficulty 10.6179 Β· 5,279,668 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dbe9447aaf91ddca2298e2ceff503a475d2bb8a17bcb4212a12f0d4e8e6d1052
View on Chainz β†—

Height

#1,534,716

Difficulty

10.617900

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e2eb3

Nonce

680,509,628

Timestamp

4/10/2016, 10:28:19 AM

Confirmations

5,279,668

Mined by

⛏️ P2SHAR8fLj57kwfJFhUsCt2FTarLr8Fo4SsiLg

Merkle Root

9e444c95c28fa5254c1d19088411e69aa5fc63fc4ba741d3466d1105788e9795
Transactions (2)
Coinbase1bd801878d9dfc…88162c2d8e101f
1 in β†’ 1 out8.9400 XPM109 B
AR8fLj57…Fo4SsiLg
d669ba6065a662…f30335be073dce
51 in β†’ 1 out1428.1283 XPM7.41 KB
AatXKS2K…Yj1J5C3D
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.

5.220 Γ— 10⁹⁴(95-digit number)
52203120699879372671…59989344266999700051
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
5.220 Γ— 10⁹⁴(95-digit number)
52203120699879372671…59989344266999700051
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.044 Γ— 10⁹⁡(96-digit number)
10440624139975874534…19978688533999400101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.088 Γ— 10⁹⁡(96-digit number)
20881248279951749068…39957377067998800201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.176 Γ— 10⁹⁡(96-digit number)
41762496559903498136…79914754135997600401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.352 Γ— 10⁹⁡(96-digit number)
83524993119806996273…59829508271995200801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.670 Γ— 10⁹⁢(97-digit number)
16704998623961399254…19659016543990401601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.340 Γ— 10⁹⁢(97-digit number)
33409997247922798509…39318033087980803201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.681 Γ— 10⁹⁢(97-digit number)
66819994495845597019…78636066175961606401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.336 Γ— 10⁹⁷(98-digit number)
13363998899169119403…57272132351923212801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.672 Γ— 10⁹⁷(98-digit number)
26727997798338238807…14544264703846425601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.345 Γ— 10⁹⁷(98-digit number)
53455995596676477615…29088529407692851201
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:57,759,132 XPMΒ·at block #6,814,383 Β· updates every 60s
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