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Home/Chain Registry/Block #1,897,954

Block #1,897,954

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/17/2016, 7:44:56 AM Β· Difficulty 10.7535 Β· 4,929,045 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e4a15f47dc3d6a601a98427fc9040ba59f4af64fbb4926043c53035bad8bea8a
View on Chainz β†—

Difficulty

10.753479

Transactions

1

Size

199 B

Version

2

Bits

0ac0e3fd

Nonce

1,071,041,970

Timestamp

12/17/2016, 7:44:56 AM

Confirmations

4,929,045

Merkle Root

4a0810cc136a0efac1093253eb357078000ac1df44fc6f0cb64c977596e1d620
Transactions (1)
Coinbase4a0810cc136a0e…4c977596e1d620
1 in β†’ 1 out8.6300 XPM109 B
APXfFP6i…3mdGqCGk
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.

5.437 Γ— 10⁹⁴(95-digit number)
54379215567042788393…48621152464030314880
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
5.437 Γ— 10⁹⁴(95-digit number)
54379215567042788393…48621152464030314881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.087 Γ— 10⁹⁡(96-digit number)
10875843113408557678…97242304928060629761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.175 Γ— 10⁹⁡(96-digit number)
21751686226817115357…94484609856121259521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.350 Γ— 10⁹⁡(96-digit number)
43503372453634230715…88969219712242519041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.700 Γ— 10⁹⁡(96-digit number)
87006744907268461430…77938439424485038081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.740 Γ— 10⁹⁢(97-digit number)
17401348981453692286…55876878848970076161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.480 Γ— 10⁹⁢(97-digit number)
34802697962907384572…11753757697940152321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.960 Γ— 10⁹⁢(97-digit number)
69605395925814769144…23507515395880304641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.392 Γ— 10⁹⁷(98-digit number)
13921079185162953828…47015030791760609281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.784 Γ— 10⁹⁷(98-digit number)
27842158370325907657…94030061583521218561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1897954

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 e4a15f47dc3d6a601a98427fc9040ba59f4af64fbb4926043c53035bad8bea8a

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 #1,897,954 on Chainz β†—
Circulating Supply:57,860,168 XPMΒ·at block #6,826,998 Β· updates every 60s
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