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Home/Chain Registry/Block #1,456,320

Block #1,456,320

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/14/2016, 1:28:52 PM Β· Difficulty 10.7436 Β· 5,386,946 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
87eccb3c80f11fb6659bcd900014880cef1a9f2d5dadceafa03f932d928b00c7
View on Chainz β†—

Difficulty

10.743553

Transactions

2

Size

1.97 KB

Version

2

Bits

0abe5983

Nonce

1,316,061,464

Timestamp

2/14/2016, 1:28:52 PM

Confirmations

5,386,946

Merkle Root

c8351db865f11458fdbb0876dd59c364543053c1a2f2b84178154dfa2bf785dd
Transactions (2)
Coinbase786f37aee02443…0fba8e3c31ab29
1 in β†’ 1 out8.6700 XPM110 B
AUoNm7dw…cmH689Se
7eb1e04138c959…1b9d476dbb1fd5
12 in β†’ 1 out99.9900 XPM1.77 KB
AP3aLPjN…qv5mAQRK
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.

3.444 Γ— 10⁹⁢(97-digit number)
34440454973364950684…12592257148651745280
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
3.444 Γ— 10⁹⁢(97-digit number)
34440454973364950684…12592257148651745281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.888 Γ— 10⁹⁢(97-digit number)
68880909946729901368…25184514297303490561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.377 Γ— 10⁹⁷(98-digit number)
13776181989345980273…50369028594606981121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.755 Γ— 10⁹⁷(98-digit number)
27552363978691960547…00738057189213962241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.510 Γ— 10⁹⁷(98-digit number)
55104727957383921094…01476114378427924481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.102 Γ— 10⁹⁸(99-digit number)
11020945591476784218…02952228756855848961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.204 Γ— 10⁹⁸(99-digit number)
22041891182953568437…05904457513711697921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.408 Γ— 10⁹⁸(99-digit number)
44083782365907136875…11808915027423395841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.816 Γ— 10⁹⁸(99-digit number)
88167564731814273751…23617830054846791681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.763 Γ— 10⁹⁹(100-digit number)
17633512946362854750…47235660109693583361
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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
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 1456320

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 87eccb3c80f11fb6659bcd900014880cef1a9f2d5dadceafa03f932d928b00c7

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 #1,456,320 on Chainz β†—
Circulating Supply:57,990,502 XPMΒ·at block #6,843,265 Β· updates every 60s
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