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Block #2,653,573

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/8/2018, 12:33:13 PM Β· Difficulty 11.7360 Β· 4,178,220 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e3ea95963f8910017b787fd54e541ee2fc83616428f40d7c147487bc07dd8aa7
View on Chainz β†—

Difficulty

11.735963

Transactions

1

Size

200 B

Version

2

Bits

0bbc680f

Nonce

269,526,665

Timestamp

5/8/2018, 12:33:13 PM

Confirmations

4,178,220

Merkle Root

675589ca9cd0e194c38e4268e58005bec6dc17488e35317d2f84f83be13ae14e
Transactions (1)
Coinbase675589ca9cd0e1…84f83be13ae14e
1 in β†’ 1 out7.2500 XPM110 B
AWKW9eFp…WGLyFyoS
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.

2.300 Γ— 10⁹⁡(96-digit number)
23003538125095254714…18827086016324409600
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
2.300 Γ— 10⁹⁡(96-digit number)
23003538125095254714…18827086016324409599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.600 Γ— 10⁹⁡(96-digit number)
46007076250190509429…37654172032648819199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.201 Γ— 10⁹⁡(96-digit number)
92014152500381018859…75308344065297638399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.840 Γ— 10⁹⁢(97-digit number)
18402830500076203771…50616688130595276799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.680 Γ— 10⁹⁢(97-digit number)
36805661000152407543…01233376261190553599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.361 Γ— 10⁹⁢(97-digit number)
73611322000304815087…02466752522381107199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.472 Γ— 10⁹⁷(98-digit number)
14722264400060963017…04933505044762214399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.944 Γ— 10⁹⁷(98-digit number)
29444528800121926034…09867010089524428799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.888 Γ— 10⁹⁷(98-digit number)
58889057600243852069…19734020179048857599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.177 Γ— 10⁹⁸(99-digit number)
11777811520048770413…39468040358097715199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.355 Γ— 10⁹⁸(99-digit number)
23555623040097540827…78936080716195430399
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 2653573

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 e3ea95963f8910017b787fd54e541ee2fc83616428f40d7c147487bc07dd8aa7

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 #2,653,573 on Chainz β†—
Circulating Supply:57,898,456 XPMΒ·at block #6,831,792 Β· updates every 60s
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