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Block #1,371,646

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/16/2015, 3:32:24 PM Β· Difficulty 10.8108 Β· 5,468,960 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
355056f52079b7c038697dfddd55d131de180d109b1483a115a8ad4800120cd7
View on Chainz β†—

Difficulty

10.810759

Transactions

1

Size

200 B

Version

2

Bits

0acf8de5

Nonce

337,684,127

Timestamp

12/16/2015, 3:32:24 PM

Confirmations

5,468,960

Merkle Root

4fa3650500494a8b7f619b7cf354dcb8ebe7eadbc4650df38cba6be80314c63c
Transactions (1)
Coinbase4fa3650500494a…ba6be80314c63c
1 in β†’ 1 out8.5400 XPM110 B
ANbQRwLP…rkzRA7zp
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.

2.385 Γ— 10⁹⁴(95-digit number)
23855787976787693776…23676404184393506480
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
2.385 Γ— 10⁹⁴(95-digit number)
23855787976787693776…23676404184393506481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.771 Γ— 10⁹⁴(95-digit number)
47711575953575387552…47352808368787012961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.542 Γ— 10⁹⁴(95-digit number)
95423151907150775105…94705616737574025921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.908 Γ— 10⁹⁡(96-digit number)
19084630381430155021…89411233475148051841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.816 Γ— 10⁹⁡(96-digit number)
38169260762860310042…78822466950296103681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.633 Γ— 10⁹⁡(96-digit number)
76338521525720620084…57644933900592207361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.526 Γ— 10⁹⁢(97-digit number)
15267704305144124016…15289867801184414721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.053 Γ— 10⁹⁢(97-digit number)
30535408610288248033…30579735602368829441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.107 Γ— 10⁹⁢(97-digit number)
61070817220576496067…61159471204737658881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.221 Γ— 10⁹⁷(98-digit number)
12214163444115299213…22318942409475317761
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 1371646

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 355056f52079b7c038697dfddd55d131de180d109b1483a115a8ad4800120cd7

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 #1,371,646 on Chainz β†—
Circulating Supply:57,969,184 XPMΒ·at block #6,840,605 Β· updates every 60s
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