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Block #1,534,714

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 10:25:16 AM Β· Difficulty 10.6182 Β· 5,290,342 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
182cb783b9d1048bc13d5567a89feb2b8c3c9994b3c1e196a00509c1417ca54d
View on Chainz β†—

Height

#1,534,714

Difficulty

10.618241

Transactions

2

Size

7.62 KB

Version

2

Bits

0a9e4509

Nonce

431,519,462

Timestamp

4/10/2016, 10:25:16 AM

Confirmations

5,290,342

Mined by

⛏️ P2SHAKvZkQyzJBiaob9jqJf7KwPnuU5DV8MKNo

Merkle Root

a0def8b99557741115e22c84037284ffc65109016e2b7d4d6caef584b5a82789
Transactions (2)
Coinbase374671ff296ea2…56676c0290f00b
1 in β†’ 1 out8.9400 XPM109 B
AKvZkQyz…5DV8MKNo
ee739d13ea89f6…e71a3a21827c70
51 in β†’ 1 out359.7934 XPM7.42 KB
APW94zty…HiTxsSa7
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.

2.029 Γ— 10⁹⁡(96-digit number)
20291847358125809603…65759820910101948801
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
2.029 Γ— 10⁹⁡(96-digit number)
20291847358125809603…65759820910101948801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.058 Γ— 10⁹⁡(96-digit number)
40583694716251619206…31519641820203897601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.116 Γ— 10⁹⁡(96-digit number)
81167389432503238412…63039283640407795201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.623 Γ— 10⁹⁢(97-digit number)
16233477886500647682…26078567280815590401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.246 Γ— 10⁹⁢(97-digit number)
32466955773001295364…52157134561631180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.493 Γ— 10⁹⁢(97-digit number)
64933911546002590729…04314269123262361601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.298 Γ— 10⁹⁷(98-digit number)
12986782309200518145…08628538246524723201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.597 Γ— 10⁹⁷(98-digit number)
25973564618401036291…17257076493049446401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.194 Γ— 10⁹⁷(98-digit number)
51947129236802072583…34514152986098892801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.038 Γ— 10⁹⁸(99-digit number)
10389425847360414516…69028305972197785601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.077 Γ— 10⁹⁸(99-digit number)
20778851694720829033…38056611944395571201
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:57,844,533 XPMΒ·at block #6,825,055 Β· updates every 60s
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