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Home/Chain Registry/Block #2,241,890

Block #2,241,890

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2017, 3:13:24 AM Β· Difficulty 10.9472 Β· 4,585,433 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1d296f556aed2e50bb2ff9fcac05f2b22fee7b5511be85d1c15c335e28d9266e
View on Chainz β†—

Difficulty

10.947176

Transactions

1

Size

242 B

Version

2

Bits

0af27a1e

Nonce

1,618,875,237

Timestamp

8/8/2017, 3:13:24 AM

Confirmations

4,585,433

Merkle Root

3fc264c0fd28d1f7451c6b84512c4246ef86290c6cb9ca46eb561272614da4ab
Transactions (1)
Coinbase3fc264c0fd28d1…561272614da4ab
1 in β†’ 2 out8.3300 XPM152 B
AY5YR3dJ…dsVboVgSAXbk7f7A…Tx7JECPG
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.

4.412 Γ— 10⁹⁡(96-digit number)
44128841491277731496…36323002592633700160
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
4.412 Γ— 10⁹⁡(96-digit number)
44128841491277731496…36323002592633700161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.825 Γ— 10⁹⁡(96-digit number)
88257682982555462993…72646005185267400321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.765 Γ— 10⁹⁢(97-digit number)
17651536596511092598…45292010370534800641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.530 Γ— 10⁹⁢(97-digit number)
35303073193022185197…90584020741069601281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.060 Γ— 10⁹⁢(97-digit number)
70606146386044370394…81168041482139202561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.412 Γ— 10⁹⁷(98-digit number)
14121229277208874078…62336082964278405121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.824 Γ— 10⁹⁷(98-digit number)
28242458554417748157…24672165928556810241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.648 Γ— 10⁹⁷(98-digit number)
56484917108835496315…49344331857113620481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.129 Γ— 10⁹⁸(99-digit number)
11296983421767099263…98688663714227240961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.259 Γ— 10⁹⁸(99-digit number)
22593966843534198526…97377327428454481921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.518 Γ— 10⁹⁸(99-digit number)
45187933687068397052…94754654856908963841
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 2241890

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 1d296f556aed2e50bb2ff9fcac05f2b22fee7b5511be85d1c15c335e28d9266e

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 #2,241,890 on Chainz β†—
Circulating Supply:57,862,697 XPMΒ·at block #6,827,322 Β· updates every 60s
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