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Home/Chain Registry/Block #2,151,532

Block #2,151,532

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/8/2017, 11:00:30 AM Β· Difficulty 10.9002 Β· 4,685,400 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aefcb29776cea206233fc0c0cd243abed7f9800afd57fb5fc404aa98864a33b0
View on Chainz β†—

Difficulty

10.900174

Transactions

2

Size

3.02 KB

Version

2

Bits

0ae671cc

Nonce

136,104,480

Timestamp

6/8/2017, 11:00:30 AM

Confirmations

4,685,400

Merkle Root

565043b3e880335783f431fee804ef7ea1b5ce6e69e07ab35bbd487eb0b761f5
Transactions (2)
Coinbase5b56468635bb1f…593d8ee7745aba
1 in β†’ 1 out8.4300 XPM110 B
ANmz9SN5…5LdNWFpi
a638955c75fcfe…9f34e9bb4f28d5
19 in β†’ 2 out152.4830 XPM2.82 KB
AcGvZhRu…evfo9pnaAUHcV5xD…n3YU8Hdh
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.

2.718 Γ— 10⁹⁴(95-digit number)
27188776310046558751…25383208579798113920
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
2.718 Γ— 10⁹⁴(95-digit number)
27188776310046558751…25383208579798113921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.437 Γ— 10⁹⁴(95-digit number)
54377552620093117503…50766417159596227841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.087 Γ— 10⁹⁡(96-digit number)
10875510524018623500…01532834319192455681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.175 Γ— 10⁹⁡(96-digit number)
21751021048037247001…03065668638384911361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.350 Γ— 10⁹⁡(96-digit number)
43502042096074494002…06131337276769822721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.700 Γ— 10⁹⁡(96-digit number)
87004084192148988005…12262674553539645441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.740 Γ— 10⁹⁢(97-digit number)
17400816838429797601…24525349107079290881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.480 Γ— 10⁹⁢(97-digit number)
34801633676859595202…49050698214158581761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.960 Γ— 10⁹⁢(97-digit number)
69603267353719190404…98101396428317163521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.392 Γ— 10⁹⁷(98-digit number)
13920653470743838080…96202792856634327041
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 2151532

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 aefcb29776cea206233fc0c0cd243abed7f9800afd57fb5fc404aa98864a33b0

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 #2,151,532 on Chainz β†—
Circulating Supply:57,939,753 XPMΒ·at block #6,836,931 Β· updates every 60s
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