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Home/Chain Registry/Block #1,408,539

Block #1,408,539

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/11/2016, 9:42:50 AM Β· Difficulty 10.8044 Β· 5,433,706 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8ed7774c1915b7c74316da83d3927c33d4af0a5bcf8a0ad1966f90219cebf8bc
View on Chainz β†—

Difficulty

10.804441

Transactions

1

Size

243 B

Version

2

Bits

0acdefda

Nonce

569,730,691

Timestamp

1/11/2016, 9:42:50 AM

Confirmations

5,433,706

Merkle Root

31794a4b31a27a692af3e6a87c9dc9963d935e5601a2c0e899b17ad5f506ee46
Transactions (1)
Coinbase31794a4b31a27a…b17ad5f506ee46
1 in β†’ 2 out8.5500 XPM152 B
AbNVgXWJ…g3uNfMnjALPu3s2c…EJXLjVFh
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.

7.954 Γ— 10⁹⁢(97-digit number)
79546830186380614996…48928327796215802880
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
7.954 Γ— 10⁹⁢(97-digit number)
79546830186380614996…48928327796215802881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.590 Γ— 10⁹⁷(98-digit number)
15909366037276122999…97856655592431605761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.181 Γ— 10⁹⁷(98-digit number)
31818732074552245998…95713311184863211521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.363 Γ— 10⁹⁷(98-digit number)
63637464149104491997…91426622369726423041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.272 Γ— 10⁹⁸(99-digit number)
12727492829820898399…82853244739452846081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.545 Γ— 10⁹⁸(99-digit number)
25454985659641796798…65706489478905692161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.090 Γ— 10⁹⁸(99-digit number)
50909971319283593597…31412978957811384321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.018 Γ— 10⁹⁹(100-digit number)
10181994263856718719…62825957915622768641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.036 Γ— 10⁹⁹(100-digit number)
20363988527713437439…25651915831245537281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.072 Γ— 10⁹⁹(100-digit number)
40727977055426874878…51303831662491074561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.145 Γ— 10⁹⁹(100-digit number)
81455954110853749756…02607663324982149121
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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
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, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 1408539

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 8ed7774c1915b7c74316da83d3927c33d4af0a5bcf8a0ad1966f90219cebf8bc

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #1,408,539 on Chainz β†—
Circulating Supply:57,982,358 XPMΒ·at block #6,842,244 Β· updates every 60s
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