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Home/Chain Registry/Block #2,123,677

Block #2,123,677

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/19/2017, 10:19:11 AM Β· Difficulty 10.9171 Β· 4,714,721 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
08171d0eb3dbb663bc4e99a6667a40838b54291e740920bcec6031544aebad69
View on Chainz β†—

Difficulty

10.917120

Transactions

1

Size

200 B

Version

2

Bits

0aeac867

Nonce

2,130,995,359

Timestamp

5/19/2017, 10:19:11 AM

Confirmations

4,714,721

Merkle Root

5bdfe8324cd3af1d9d5a36f3ff255357adb3292ffb7cacb66379aeee37d56215
Transactions (1)
Coinbase5bdfe8324cd3af…79aeee37d56215
1 in β†’ 1 out8.3800 XPM110 B
AaxBhhE4…B34hAv7V
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.

1.775 Γ— 10⁹⁴(95-digit number)
17757125567657347557…74234366059506485760
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
1.775 Γ— 10⁹⁴(95-digit number)
17757125567657347557…74234366059506485761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.551 Γ— 10⁹⁴(95-digit number)
35514251135314695114…48468732119012971521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.102 Γ— 10⁹⁴(95-digit number)
71028502270629390228…96937464238025943041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.420 Γ— 10⁹⁡(96-digit number)
14205700454125878045…93874928476051886081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.841 Γ— 10⁹⁡(96-digit number)
28411400908251756091…87749856952103772161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.682 Γ— 10⁹⁡(96-digit number)
56822801816503512183…75499713904207544321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.136 Γ— 10⁹⁢(97-digit number)
11364560363300702436…50999427808415088641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.272 Γ— 10⁹⁢(97-digit number)
22729120726601404873…01998855616830177281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.545 Γ— 10⁹⁢(97-digit number)
45458241453202809746…03997711233660354561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.091 Γ— 10⁹⁢(97-digit number)
90916482906405619492…07995422467320709121
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 2123677

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 08171d0eb3dbb663bc4e99a6667a40838b54291e740920bcec6031544aebad69

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 #2,123,677 on Chainz β†—
Circulating Supply:57,951,458 XPMΒ·at block #6,838,397 Β· updates every 60s
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