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Home/Chain Registry/Block #2,156,383

Block #2,156,383

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/11/2017, 2:27:44 PM Β· Difficulty 10.9064 Β· 4,687,323 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9c61bed854f685c0c64ab007fe6b19f2af03acd81348f080ae856cc3f6678490
View on Chainz β†—

Difficulty

10.906433

Transactions

1

Size

199 B

Version

2

Bits

0ae80bf6

Nonce

432,132,821

Timestamp

6/11/2017, 2:27:44 PM

Confirmations

4,687,323

Merkle Root

eaaa127c12b35c558992729b622f5092b4cfa4d2a9f0d7252c7303bcc357f495
Transactions (1)
Coinbaseeaaa127c12b35c…7303bcc357f495
1 in β†’ 1 out8.3900 XPM109 B
AVxNCNCt…R7YEtCKe
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.

8.978 Γ— 10⁹⁴(95-digit number)
89781882418981145520…84506225787620520000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
8.978 Γ— 10⁹⁴(95-digit number)
89781882418981145520…84506225787620519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.795 Γ— 10⁹⁡(96-digit number)
17956376483796229104…69012451575241039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.591 Γ— 10⁹⁡(96-digit number)
35912752967592458208…38024903150482079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.182 Γ— 10⁹⁡(96-digit number)
71825505935184916416…76049806300964159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.436 Γ— 10⁹⁢(97-digit number)
14365101187036983283…52099612601928319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.873 Γ— 10⁹⁢(97-digit number)
28730202374073966566…04199225203856639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.746 Γ— 10⁹⁢(97-digit number)
57460404748147933133…08398450407713279999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.149 Γ— 10⁹⁷(98-digit number)
11492080949629586626…16796900815426559999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.298 Γ— 10⁹⁷(98-digit number)
22984161899259173253…33593801630853119999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.596 Γ— 10⁹⁷(98-digit number)
45968323798518346506…67187603261706239999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.193 Γ— 10⁹⁷(98-digit number)
91936647597036693013…34375206523412479999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2156383

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 9c61bed854f685c0c64ab007fe6b19f2af03acd81348f080ae856cc3f6678490

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 #2,156,383 on Chainz β†—
Circulating Supply:57,994,017 XPMΒ·at block #6,843,705 Β· updates every 60s
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