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Block #1,421,425

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/20/2016, 4:14:49 PM Β· Difficulty 10.7859 Β· 5,420,139 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5dc637e09d32c1b23f846ea5802e4ecfd80a02875c1eed4fb99b613e7d7325c1
View on Chainz β†—

Difficulty

10.785932

Transactions

1

Size

200 B

Version

2

Bits

0ac932d5

Nonce

1,374,484,750

Timestamp

1/20/2016, 4:14:49 PM

Confirmations

5,420,139

Merkle Root

21ef0cd0b8861b41c30b4e5f186428dc006d454695aa85e9116b12e65c4be9fb
Transactions (1)
Coinbase21ef0cd0b8861b…6b12e65c4be9fb
1 in β†’ 1 out8.5800 XPM110 B
AYDYwoAe…SaqsPdvt
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.

2.451 Γ— 10⁹⁴(95-digit number)
24511698215863918461…15674177224531630080
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
2.451 Γ— 10⁹⁴(95-digit number)
24511698215863918461…15674177224531630081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.902 Γ— 10⁹⁴(95-digit number)
49023396431727836923…31348354449063260161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.804 Γ— 10⁹⁴(95-digit number)
98046792863455673847…62696708898126520321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.960 Γ— 10⁹⁡(96-digit number)
19609358572691134769…25393417796253040641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.921 Γ— 10⁹⁡(96-digit number)
39218717145382269538…50786835592506081281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.843 Γ— 10⁹⁡(96-digit number)
78437434290764539077…01573671185012162561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.568 Γ— 10⁹⁢(97-digit number)
15687486858152907815…03147342370024325121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.137 Γ— 10⁹⁢(97-digit number)
31374973716305815631…06294684740048650241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.274 Γ— 10⁹⁢(97-digit number)
62749947432611631262…12589369480097300481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.254 Γ— 10⁹⁷(98-digit number)
12549989486522326252…25178738960194600961
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 1421425

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 5dc637e09d32c1b23f846ea5802e4ecfd80a02875c1eed4fb99b613e7d7325c1

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 #1,421,425 on Chainz β†—
Circulating Supply:57,976,896 XPMΒ·at block #6,841,563 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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