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Block #1,479,071

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/1/2016, 6:38:30 PM Β· Difficulty 10.7121 Β· 5,362,835 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
43a40e713d79864fb054d12ba755b19ae9946dffd745098084503d6a070a9fab
View on Chainz β†—

Height

#1,479,071

Difficulty

10.712142

Transactions

2

Size

1.14 KB

Version

2

Bits

0ab64ee8

Nonce

89,592,621

Timestamp

3/1/2016, 6:38:30 PM

Confirmations

5,362,835

Mined by

⛏️ P2SHAG32F9wNkwxMFB9QWZrTvSPq5nV7JmmVRn

Merkle Root

c350eed95c90c776d25dfc1b0dafaaa38f422e455c4748e6c22450837b251429
Transactions (2)
Coinbase9f0d0badb2dbde…489d2df5c50c96
1 in β†’ 1 out8.7100 XPM109 B
AG32F9wN…V7JmmVRn
9bf0db938268d8…06eedaa3878a05
6 in β†’ 2 out43.2865 XPM965 B
AWMqWz7H…ipMpM8WRAGtsk7LU…v7dya8x4
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.

9.631 Γ— 10⁹¹(92-digit number)
96312461618053595444…04444785389987281831
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
9.631 Γ— 10⁹¹(92-digit number)
96312461618053595444…04444785389987281831
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.926 Γ— 10⁹²(93-digit number)
19262492323610719088…08889570779974563661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.852 Γ— 10⁹²(93-digit number)
38524984647221438177…17779141559949127321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.704 Γ— 10⁹²(93-digit number)
77049969294442876355…35558283119898254641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.540 Γ— 10⁹³(94-digit number)
15409993858888575271…71116566239796509281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.081 Γ— 10⁹³(94-digit number)
30819987717777150542…42233132479593018561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.163 Γ— 10⁹³(94-digit number)
61639975435554301084…84466264959186037121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.232 Γ— 10⁹⁴(95-digit number)
12327995087110860216…68932529918372074241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.465 Γ— 10⁹⁴(95-digit number)
24655990174221720433…37865059836744148481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.931 Γ— 10⁹⁴(95-digit number)
49311980348443440867…75730119673488296961
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:57,979,622 XPMΒ·at block #6,841,905 Β· updates every 60s
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