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Block #1,612,850

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/3/2016, 9:13:13 PM Β· Difficulty 10.6004 Β· 5,229,944 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
85bd004b4248ae8be1dbc5190428838e71cfed21d417ed4afe10abe23e2df8af
View on Chainz β†—

Difficulty

10.600391

Transactions

1

Size

199 B

Version

2

Bits

0a99b33f

Nonce

316,213,654

Timestamp

6/3/2016, 9:13:13 PM

Confirmations

5,229,944

Merkle Root

f98a82c9949852d09435dc7ffbe30235f7ff7eee58337d06d4075416b63a3f72
Transactions (1)
Coinbasef98a82c9949852…075416b63a3f72
1 in β†’ 1 out8.8900 XPM109 B
AXajSxbZ…iKGz9181
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.

2.449 Γ— 10⁹⁴(95-digit number)
24490383665716019080…91007802532870673600
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
2.449 Γ— 10⁹⁴(95-digit number)
24490383665716019080…91007802532870673601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.898 Γ— 10⁹⁴(95-digit number)
48980767331432038160…82015605065741347201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.796 Γ— 10⁹⁴(95-digit number)
97961534662864076321…64031210131482694401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.959 Γ— 10⁹⁡(96-digit number)
19592306932572815264…28062420262965388801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.918 Γ— 10⁹⁡(96-digit number)
39184613865145630528…56124840525930777601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.836 Γ— 10⁹⁡(96-digit number)
78369227730291261057…12249681051861555201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.567 Γ— 10⁹⁢(97-digit number)
15673845546058252211…24499362103723110401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.134 Γ— 10⁹⁢(97-digit number)
31347691092116504422…48998724207446220801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.269 Γ— 10⁹⁢(97-digit number)
62695382184233008845…97997448414892441601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.253 Γ— 10⁹⁷(98-digit number)
12539076436846601769…95994896829784883201
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 1612850

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 85bd004b4248ae8be1dbc5190428838e71cfed21d417ed4afe10abe23e2df8af

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 #1,612,850 on Chainz β†—
Circulating Supply:57,986,692 XPMΒ·at block #6,842,793 Β· updates every 60s
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