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Home/Chain Registry/Block #2,654,974

Block #2,654,974

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/9/2018, 7:16:39 PM Β· Difficulty 11.7117 Β· 4,185,481 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eb841757d9f7c3f9a6f564b03ab6898ab200e386d737c7285a8b822fcceeb7e3
View on Chainz β†—

Difficulty

11.711655

Transactions

1

Size

201 B

Version

2

Bits

0bb62efe

Nonce

1,032,617,512

Timestamp

5/9/2018, 7:16:39 PM

Confirmations

4,185,481

Merkle Root

878b222891d36f1532faf1d128cc745d7be248a3987f70d7af26de84b10a7863
Transactions (1)
Coinbase878b222891d36f…26de84b10a7863
1 in β†’ 1 out7.2800 XPM110 B
ATBGxdde…qGyKrxBz
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.

1.043 Γ— 10⁹⁷(98-digit number)
10431018709290451729…49609562650930391040
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
1.043 Γ— 10⁹⁷(98-digit number)
10431018709290451729…49609562650930391041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.086 Γ— 10⁹⁷(98-digit number)
20862037418580903459…99219125301860782081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.172 Γ— 10⁹⁷(98-digit number)
41724074837161806918…98438250603721564161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.344 Γ— 10⁹⁷(98-digit number)
83448149674323613836…96876501207443128321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.668 Γ— 10⁹⁸(99-digit number)
16689629934864722767…93753002414886256641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.337 Γ— 10⁹⁸(99-digit number)
33379259869729445534…87506004829772513281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.675 Γ— 10⁹⁸(99-digit number)
66758519739458891069…75012009659545026561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.335 Γ— 10⁹⁹(100-digit number)
13351703947891778213…50024019319090053121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.670 Γ— 10⁹⁹(100-digit number)
26703407895783556427…00048038638180106241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.340 Γ— 10⁹⁹(100-digit number)
53406815791567112855…00096077276360212481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.068 Γ— 10¹⁰⁰(101-digit number)
10681363158313422571…00192154552720424961
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 2654974

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 eb841757d9f7c3f9a6f564b03ab6898ab200e386d737c7285a8b822fcceeb7e3

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 #2,654,974 on Chainz β†—
Circulating Supply:57,967,971 XPMΒ·at block #6,840,454 Β· updates every 60s
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