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Home/Chain Registry/Block #2,457,084

Block #2,457,084

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/4/2018, 10:17:33 AM Β· Difficulty 10.9538 Β· 4,386,956 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bdf29e2ea4473ee66cf2b818c1a2be8a9f037301bc6a12d2bce31a12ff4e4417
View on Chainz β†—

Difficulty

10.953779

Transactions

1

Size

200 B

Version

2

Bits

0af42add

Nonce

173,560,709

Timestamp

1/4/2018, 10:17:33 AM

Confirmations

4,386,956

Merkle Root

60988f761282f92d9db0f328ef2ccbe81ff92d1cfd18c458e0e1707c499a33fe
Transactions (1)
Coinbase60988f761282f9…e1707c499a33fe
1 in β†’ 1 out8.3200 XPM110 B
AJSb5S8k…kkAu2xf6
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.

6.199 Γ— 10⁹⁴(95-digit number)
61999134267030355217…68814379637811625520
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
6.199 Γ— 10⁹⁴(95-digit number)
61999134267030355217…68814379637811625521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.239 Γ— 10⁹⁡(96-digit number)
12399826853406071043…37628759275623251041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.479 Γ— 10⁹⁡(96-digit number)
24799653706812142087…75257518551246502081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.959 Γ— 10⁹⁡(96-digit number)
49599307413624284174…50515037102493004161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.919 Γ— 10⁹⁡(96-digit number)
99198614827248568348…01030074204986008321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.983 Γ— 10⁹⁢(97-digit number)
19839722965449713669…02060148409972016641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.967 Γ— 10⁹⁢(97-digit number)
39679445930899427339…04120296819944033281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.935 Γ— 10⁹⁢(97-digit number)
79358891861798854678…08240593639888066561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.587 Γ— 10⁹⁷(98-digit number)
15871778372359770935…16481187279776133121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.174 Γ— 10⁹⁷(98-digit number)
31743556744719541871…32962374559552266241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.348 Γ— 10⁹⁷(98-digit number)
63487113489439083742…65924749119104532481
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 2457084

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 bdf29e2ea4473ee66cf2b818c1a2be8a9f037301bc6a12d2bce31a12ff4e4417

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 #2,457,084 on Chainz β†—
Circulating Supply:57,996,689 XPMΒ·at block #6,844,039 Β· updates every 60s
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