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Home/Chain Registry/Block #1,501,991

Block #1,501,991

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/18/2016, 11:00:17 AM Β· Difficulty 10.6428 Β· 5,331,320 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
35e65e2732b3f1dde492d92c11dc29ff7975e608a33812a582e59c4cb02abb02
View on Chainz β†—

Difficulty

10.642807

Transactions

1

Size

200 B

Version

2

Bits

0aa48f00

Nonce

652,913,984

Timestamp

3/18/2016, 11:00:17 AM

Confirmations

5,331,320

Merkle Root

2f172f7681bb21bbd7b0f02e2563b18e91b90199d57b49063d9f6b4a2989c572
Transactions (1)
Coinbase2f172f7681bb21…9f6b4a2989c572
1 in β†’ 1 out8.8100 XPM109 B
AL2s8Pch…4rxCrZCx
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.

1.481 Γ— 10⁹⁷(98-digit number)
14815655507312268499…08813929434467450880
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
1.481 Γ— 10⁹⁷(98-digit number)
14815655507312268499…08813929434467450881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.963 Γ— 10⁹⁷(98-digit number)
29631311014624536998…17627858868934901761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.926 Γ— 10⁹⁷(98-digit number)
59262622029249073997…35255717737869803521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.185 Γ— 10⁹⁸(99-digit number)
11852524405849814799…70511435475739607041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.370 Γ— 10⁹⁸(99-digit number)
23705048811699629598…41022870951479214081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.741 Γ— 10⁹⁸(99-digit number)
47410097623399259197…82045741902958428161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.482 Γ— 10⁹⁸(99-digit number)
94820195246798518395…64091483805916856321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.896 Γ— 10⁹⁹(100-digit number)
18964039049359703679…28182967611833712641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.792 Γ— 10⁹⁹(100-digit number)
37928078098719407358…56365935223667425281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.585 Γ— 10⁹⁹(100-digit number)
75856156197438814716…12731870447334850561
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 1501991

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 35e65e2732b3f1dde492d92c11dc29ff7975e608a33812a582e59c4cb02abb02

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 #1,501,991 on Chainz β†—
Circulating Supply:57,910,679 XPMΒ·at block #6,833,310 Β· updates every 60s
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