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Home/Chain Registry/Block #1,734,142

Block #1,734,142

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/25/2016, 10:45:45 PM Β· Difficulty 10.7181 Β· 5,107,119 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
101ded06ca830fdb288de9c7a65630e0ff241504ba5d8d9f6cb1f2710e9f2659
View on Chainz β†—

Difficulty

10.718051

Transactions

1

Size

201 B

Version

2

Bits

0ab7d22a

Nonce

72,842,659

Timestamp

8/25/2016, 10:45:45 PM

Confirmations

5,107,119

Merkle Root

e15f9b3a9a330bb907f7bc557b761c46bfaa9edd0feee209e7dd50c5814df0b8
Transactions (1)
Coinbasee15f9b3a9a330b…dd50c5814df0b8
1 in β†’ 1 out8.6900 XPM110 B
AJmKH58a…SmbiSGgh
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.

7.929 Γ— 10⁹⁡(96-digit number)
79296968474937977480…50668628817557130240
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
7.929 Γ— 10⁹⁡(96-digit number)
79296968474937977480…50668628817557130241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.585 Γ— 10⁹⁢(97-digit number)
15859393694987595496…01337257635114260481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.171 Γ— 10⁹⁢(97-digit number)
31718787389975190992…02674515270228520961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.343 Γ— 10⁹⁢(97-digit number)
63437574779950381984…05349030540457041921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.268 Γ— 10⁹⁷(98-digit number)
12687514955990076396…10698061080914083841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.537 Γ— 10⁹⁷(98-digit number)
25375029911980152793…21396122161828167681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.075 Γ— 10⁹⁷(98-digit number)
50750059823960305587…42792244323656335361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.015 Γ— 10⁹⁸(99-digit number)
10150011964792061117…85584488647312670721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.030 Γ— 10⁹⁸(99-digit number)
20300023929584122235…71168977294625341441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.060 Γ— 10⁹⁸(99-digit number)
40600047859168244470…42337954589250682881
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 1734142

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 101ded06ca830fdb288de9c7a65630e0ff241504ba5d8d9f6cb1f2710e9f2659

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 #1,734,142 on Chainz β†—
Circulating Supply:57,974,453 XPMΒ·at block #6,841,260 Β· updates every 60s
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