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Home/Chain Registry/Block #2,104,525

Block #2,104,525

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/7/2017, 9:50:17 AM Β· Difficulty 10.8798 Β· 4,732,021 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
42370261f89960340725c1b813914d1b933776656bd3e5eaef0cab90f2a8f700
View on Chainz β†—

Difficulty

10.879776

Transactions

1

Size

242 B

Version

2

Bits

0ae13906

Nonce

362,387,253

Timestamp

5/7/2017, 9:50:17 AM

Confirmations

4,732,021

Merkle Root

2be7561bb67fe4fbee52fa32f65514a2f6b238ea6ed48b86152a9c4a87b820fe
Transactions (1)
Coinbase2be7561bb67fe4…2a9c4a87b820fe
1 in β†’ 2 out8.4300 XPM152 B
AdVLhe2j…QVKRTK6uALPu3s2c…EJXLjVFh
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.

1.675 Γ— 10⁹⁡(96-digit number)
16755967984622526624…19985542578441778560
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
1.675 Γ— 10⁹⁡(96-digit number)
16755967984622526624…19985542578441778561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.351 Γ— 10⁹⁡(96-digit number)
33511935969245053249…39971085156883557121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.702 Γ— 10⁹⁡(96-digit number)
67023871938490106499…79942170313767114241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.340 Γ— 10⁹⁢(97-digit number)
13404774387698021299…59884340627534228481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.680 Γ— 10⁹⁢(97-digit number)
26809548775396042599…19768681255068456961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.361 Γ— 10⁹⁢(97-digit number)
53619097550792085199…39537362510136913921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.072 Γ— 10⁹⁷(98-digit number)
10723819510158417039…79074725020273827841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.144 Γ— 10⁹⁷(98-digit number)
21447639020316834079…58149450040547655681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.289 Γ— 10⁹⁷(98-digit number)
42895278040633668159…16298900081095311361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.579 Γ— 10⁹⁷(98-digit number)
85790556081267336318…32597800162190622721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.715 Γ— 10⁹⁸(99-digit number)
17158111216253467263…65195600324381245441
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 2104525

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 42370261f89960340725c1b813914d1b933776656bd3e5eaef0cab90f2a8f700

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 #2,104,525 on Chainz β†—
Circulating Supply:57,936,633 XPMΒ·at block #6,836,545 Β· updates every 60s
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