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Home/Chain Registry/Block #2,135,406

Block #2,135,406

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/28/2017, 4:54:00 AM Β· Difficulty 10.9012 Β· 4,707,699 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f5e74f4490eee6f6949d661b2e5ae12cc0c6e4336814ba8e2ac8fdc9289b6b14
View on Chainz β†—

Difficulty

10.901206

Transactions

1

Size

200 B

Version

2

Bits

0ae6b570

Nonce

2,047,938,156

Timestamp

5/28/2017, 4:54:00 AM

Confirmations

4,707,699

Merkle Root

da427024af5e1291ace7490e05ecea3f1012899e06ffe6283b4d473bf36f5633
Transactions (1)
Coinbaseda427024af5e12…4d473bf36f5633
1 in β†’ 1 out8.4000 XPM110 B
AXFX9zJd…C994NgRa
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.

7.409 Γ— 10⁹⁡(96-digit number)
74092181840472649060…75296621298682789120
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
7.409 Γ— 10⁹⁡(96-digit number)
74092181840472649060…75296621298682789121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.481 Γ— 10⁹⁢(97-digit number)
14818436368094529812…50593242597365578241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.963 Γ— 10⁹⁢(97-digit number)
29636872736189059624…01186485194731156481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.927 Γ— 10⁹⁢(97-digit number)
59273745472378119248…02372970389462312961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.185 Γ— 10⁹⁷(98-digit number)
11854749094475623849…04745940778924625921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.370 Γ— 10⁹⁷(98-digit number)
23709498188951247699…09491881557849251841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.741 Γ— 10⁹⁷(98-digit number)
47418996377902495398…18983763115698503681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.483 Γ— 10⁹⁷(98-digit number)
94837992755804990797…37967526231397007361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.896 Γ— 10⁹⁸(99-digit number)
18967598551160998159…75935052462794014721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.793 Γ— 10⁹⁸(99-digit number)
37935197102321996319…51870104925588029441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.587 Γ— 10⁹⁸(99-digit number)
75870394204643992638…03740209851176058881
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 2135406

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 f5e74f4490eee6f6949d661b2e5ae12cc0c6e4336814ba8e2ac8fdc9289b6b14

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 #2,135,406 on Chainz β†—
Circulating Supply:57,989,204 XPMΒ·at block #6,843,104 Β· updates every 60s
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