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Block #1,937,051

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/13/2017, 6:33:00 AM Β· Difficulty 10.7684 Β· 4,905,432 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
34e46006ef11307fe861560ebab343c17d69d9d5a9aa2cf9e3ab5769ce44f609
View on Chainz β†—

Difficulty

10.768420

Transactions

1

Size

198 B

Version

2

Bits

0ac4b72e

Nonce

1,903,623,585

Timestamp

1/13/2017, 6:33:00 AM

Confirmations

4,905,432

Merkle Root

718c6518f247b5efc8f3eafed52e438c09b07b15fe83e1a2e1b2da5023d0f5d5
Transactions (1)
Coinbase718c6518f247b5…b2da5023d0f5d5
1 in β†’ 1 out8.6100 XPM109 B
AQdJJQkS…bR9NegFy
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.

1.078 Γ— 10⁹³(94-digit number)
10782338653347911956…67699499811376999320
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
1.078 Γ— 10⁹³(94-digit number)
10782338653347911956…67699499811376999321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.156 Γ— 10⁹³(94-digit number)
21564677306695823913…35398999622753998641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.312 Γ— 10⁹³(94-digit number)
43129354613391647827…70797999245507997281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.625 Γ— 10⁹³(94-digit number)
86258709226783295654…41595998491015994561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.725 Γ— 10⁹⁴(95-digit number)
17251741845356659130…83191996982031989121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.450 Γ— 10⁹⁴(95-digit number)
34503483690713318261…66383993964063978241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.900 Γ— 10⁹⁴(95-digit number)
69006967381426636523…32767987928127956481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.380 Γ— 10⁹⁡(96-digit number)
13801393476285327304…65535975856255912961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.760 Γ— 10⁹⁡(96-digit number)
27602786952570654609…31071951712511825921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.520 Γ— 10⁹⁡(96-digit number)
55205573905141309218…62143903425023651841
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 1937051

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 34e46006ef11307fe861560ebab343c17d69d9d5a9aa2cf9e3ab5769ce44f609

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 #1,937,051 on Chainz β†—
Circulating Supply:57,984,282 XPMΒ·at block #6,842,482 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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