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Home/Chain Registry/Block #1,656,448

Block #1,656,448

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/1/2016, 6:09:40 PM Β· Difficulty 10.7999 Β· 5,156,233 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5dfd518655dece475b4d098a9337cb9fc71d48888b57187518611f6ecddf854d
View on Chainz β†—

Difficulty

10.799944

Transactions

1

Size

242 B

Version

2

Bits

0accc91f

Nonce

680,923,385

Timestamp

7/1/2016, 6:09:40 PM

Confirmations

5,156,233

Merkle Root

44aff8bde32846d1cf9e53e6dc04c4af3ce20cac8546997a44e9598848f15898
Transactions (1)
Coinbase44aff8bde32846…e9598848f15898
1 in β†’ 2 out8.5600 XPM152 B
AJgZBh3x…9DpUcwi5ALPu3s2c…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.

8.148 Γ— 10⁹⁴(95-digit number)
81487723608862308217…35632926817003332220
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
8.148 Γ— 10⁹⁴(95-digit number)
81487723608862308217…35632926817003332221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.629 Γ— 10⁹⁡(96-digit number)
16297544721772461643…71265853634006664441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.259 Γ— 10⁹⁡(96-digit number)
32595089443544923287…42531707268013328881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.519 Γ— 10⁹⁡(96-digit number)
65190178887089846574…85063414536026657761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.303 Γ— 10⁹⁢(97-digit number)
13038035777417969314…70126829072053315521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.607 Γ— 10⁹⁢(97-digit number)
26076071554835938629…40253658144106631041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.215 Γ— 10⁹⁢(97-digit number)
52152143109671877259…80507316288213262081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.043 Γ— 10⁹⁷(98-digit number)
10430428621934375451…61014632576426524161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.086 Γ— 10⁹⁷(98-digit number)
20860857243868750903…22029265152853048321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.172 Γ— 10⁹⁷(98-digit number)
41721714487737501807…44058530305706096641
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 1656448

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 5dfd518655dece475b4d098a9337cb9fc71d48888b57187518611f6ecddf854d

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 #1,656,448 on Chainz β†—
Circulating Supply:57,745,481 XPMΒ·at block #6,812,680 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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