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Home/Chain Registry/Block #2,551,380

Block #2,551,380

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/6/2018, 5:59:35 AM Β· Difficulty 10.9893 Β· 4,279,683 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a05036f80b63e68645e105871adba39f4089418d07a8b5d951e69463dc92ca01
View on Chainz β†—

Difficulty

10.989340

Transactions

1

Size

200 B

Version

2

Bits

0afd455d

Nonce

409,076,876

Timestamp

3/6/2018, 5:59:35 AM

Confirmations

4,279,683

Merkle Root

b1db0dde0b83d1ad496ea56ebc46889433c2a2245c461d9a35b47addcf83a3ce
Transactions (1)
Coinbaseb1db0dde0b83d1…b47addcf83a3ce
1 in β†’ 1 out8.2700 XPM110 B
AbQLBVdw…Wth93nog
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.

1.521 Γ— 10⁹⁡(96-digit number)
15214041809876424418…88869895197350839680
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
1.521 Γ— 10⁹⁡(96-digit number)
15214041809876424418…88869895197350839681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.042 Γ— 10⁹⁡(96-digit number)
30428083619752848836…77739790394701679361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.085 Γ— 10⁹⁡(96-digit number)
60856167239505697673…55479580789403358721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.217 Γ— 10⁹⁢(97-digit number)
12171233447901139534…10959161578806717441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.434 Γ— 10⁹⁢(97-digit number)
24342466895802279069…21918323157613434881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.868 Γ— 10⁹⁢(97-digit number)
48684933791604558138…43836646315226869761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.736 Γ— 10⁹⁢(97-digit number)
97369867583209116277…87673292630453739521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.947 Γ— 10⁹⁷(98-digit number)
19473973516641823255…75346585260907479041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.894 Γ— 10⁹⁷(98-digit number)
38947947033283646511…50693170521814958081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.789 Γ— 10⁹⁷(98-digit number)
77895894066567293022…01386341043629916161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.557 Γ— 10⁹⁸(99-digit number)
15579178813313458604…02772682087259832321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2551380

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 a05036f80b63e68645e105871adba39f4089418d07a8b5d951e69463dc92ca01

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 #2,551,380 on Chainz β†—
Circulating Supply:57,892,643 XPMΒ·at block #6,831,062 Β· updates every 60s
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