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Block #2,648,045

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 6:24:46 AM Β· Difficulty 11.7653 Β· 4,184,754 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
42fc8af9515838aec2ada3373cfd0e2db1b6cd48566bf1f8516044017c46b692
View on Chainz β†—

Difficulty

11.765320

Transactions

1

Size

201 B

Version

2

Bits

0bc3ec06

Nonce

702,385,180

Timestamp

5/4/2018, 6:24:46 AM

Confirmations

4,184,754

Merkle Root

bf45972e9ea024114e8bd9695285ef0d9368334aff6fc280cde8b6870529339f
Transactions (1)
Coinbasebf45972e9ea024…e8b6870529339f
1 in β†’ 1 out7.2100 XPM110 B
AVhNqM1q…eMnLrqTV
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.

4.640 Γ— 10⁹⁢(97-digit number)
46407422331808120929…54450239792090421760
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.640 Γ— 10⁹⁢(97-digit number)
46407422331808120929…54450239792090421759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.281 Γ— 10⁹⁢(97-digit number)
92814844663616241859…08900479584180843519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.856 Γ— 10⁹⁷(98-digit number)
18562968932723248371…17800959168361687039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.712 Γ— 10⁹⁷(98-digit number)
37125937865446496743…35601918336723374079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.425 Γ— 10⁹⁷(98-digit number)
74251875730892993487…71203836673446748159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.485 Γ— 10⁹⁸(99-digit number)
14850375146178598697…42407673346893496319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.970 Γ— 10⁹⁸(99-digit number)
29700750292357197395…84815346693786992639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.940 Γ— 10⁹⁸(99-digit number)
59401500584714394790…69630693387573985279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.188 Γ— 10⁹⁹(100-digit number)
11880300116942878958…39261386775147970559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.376 Γ— 10⁹⁹(100-digit number)
23760600233885757916…78522773550295941119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.752 Γ— 10⁹⁹(100-digit number)
47521200467771515832…57045547100591882239
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2648045

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 42fc8af9515838aec2ada3373cfd0e2db1b6cd48566bf1f8516044017c46b692

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 #2,648,045 on Chainz β†—
Circulating Supply:57,906,561 XPMΒ·at block #6,832,798 Β· updates every 60s
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