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Home/Chain Registry/Block #2,648,706

Block #2,648,706

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/4/2018, 5:00:14 PM Β· Difficulty 11.7665 Β· 4,183,143 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
249bc24f27027b9894d36aa37e686c7bc7e5e3c5b0dfd8fbf16f27e553af458c
View on Chainz β†—

Difficulty

11.766507

Transactions

1

Size

200 B

Version

2

Bits

0bc439cb

Nonce

1,996,592,789

Timestamp

5/4/2018, 5:00:14 PM

Confirmations

4,183,143

Merkle Root

31a8586f7642f4d33460368289ceb0fad5ee986ca33e6f0131e34e982ce88a96
Transactions (1)
Coinbase31a8586f7642f4…e34e982ce88a96
1 in β†’ 1 out7.2100 XPM109 B
AKigabZ9…NpyMtUvk
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.

1.291 Γ— 10⁹⁷(98-digit number)
12910881007541480924…84000165901205831680
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
1.291 Γ— 10⁹⁷(98-digit number)
12910881007541480924…84000165901205831681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.582 Γ— 10⁹⁷(98-digit number)
25821762015082961848…68000331802411663361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.164 Γ— 10⁹⁷(98-digit number)
51643524030165923697…36000663604823326721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.032 Γ— 10⁹⁸(99-digit number)
10328704806033184739…72001327209646653441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.065 Γ— 10⁹⁸(99-digit number)
20657409612066369478…44002654419293306881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.131 Γ— 10⁹⁸(99-digit number)
41314819224132738957…88005308838586613761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.262 Γ— 10⁹⁸(99-digit number)
82629638448265477915…76010617677173227521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.652 Γ— 10⁹⁹(100-digit number)
16525927689653095583…52021235354346455041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.305 Γ— 10⁹⁹(100-digit number)
33051855379306191166…04042470708692910081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.610 Γ— 10⁹⁹(100-digit number)
66103710758612382332…08084941417385820161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.322 Γ— 10¹⁰⁰(101-digit number)
13220742151722476466…16169882834771640321
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 2648706

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 249bc24f27027b9894d36aa37e686c7bc7e5e3c5b0dfd8fbf16f27e553af458c

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 #2,648,706 on Chainz β†—
Circulating Supply:57,898,913 XPMΒ·at block #6,831,848 Β· updates every 60s
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