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Home/Chain Registry/Block #2,639,754

Block #2,639,754

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 6:33:01 PM Β· Difficulty 11.5516 Β· 4,202,087 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6e30b55be9e6871698bdcfaea4f1bfedac9fd5e8a039b7fc5c16db215ccee8ff
View on Chainz β†—

Difficulty

11.551611

Transactions

1

Size

201 B

Version

2

Bits

0b8d3667

Nonce

401,628,902

Timestamp

4/30/2018, 6:33:01 PM

Confirmations

4,202,087

Merkle Root

feaea95026934b14eb7490f80ffc41c3cea4758b2ec2712d8907ce9bcecbf277
Transactions (1)
Coinbasefeaea95026934b…07ce9bcecbf277
1 in β†’ 1 out7.4800 XPM110 B
ASQAVNEL…XvneQq3d
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.

1.314 Γ— 10⁹⁢(97-digit number)
13144674315420544219…66659855812171678560
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
1.314 Γ— 10⁹⁢(97-digit number)
13144674315420544219…66659855812171678561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.628 Γ— 10⁹⁢(97-digit number)
26289348630841088438…33319711624343357121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.257 Γ— 10⁹⁢(97-digit number)
52578697261682176876…66639423248686714241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.051 Γ— 10⁹⁷(98-digit number)
10515739452336435375…33278846497373428481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.103 Γ— 10⁹⁷(98-digit number)
21031478904672870750…66557692994746856961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.206 Γ— 10⁹⁷(98-digit number)
42062957809345741501…33115385989493713921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.412 Γ— 10⁹⁷(98-digit number)
84125915618691483002…66230771978987427841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.682 Γ— 10⁹⁸(99-digit number)
16825183123738296600…32461543957974855681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.365 Γ— 10⁹⁸(99-digit number)
33650366247476593200…64923087915949711361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.730 Γ— 10⁹⁸(99-digit number)
67300732494953186401…29846175831899422721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.346 Γ— 10⁹⁹(100-digit number)
13460146498990637280…59692351663798845441
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 2639754

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 6e30b55be9e6871698bdcfaea4f1bfedac9fd5e8a039b7fc5c16db215ccee8ff

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 #2,639,754 on Chainz β†—
Circulating Supply:57,979,102 XPMΒ·at block #6,841,840 Β· updates every 60s
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