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Home/Chain Registry/Block #2,991,153

Block #2,991,153

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/1/2019, 4:14:45 PM Β· Difficulty 11.2587 Β· 3,849,601 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9d903018ab47e6e8cf833b3e74eed64f8424cf25f7e789ff7cdb3dd8dac8188c
View on Chainz β†—

Difficulty

11.258691

Transactions

1

Size

200 B

Version

2

Bits

0b423996

Nonce

1,305,033,545

Timestamp

1/1/2019, 4:14:45 PM

Confirmations

3,849,601

Merkle Root

02dda4032a952f7fbbab10c62fd7354fd105640d3ba68f6b0aa608995731b32f
Transactions (1)
Coinbase02dda4032a952f…a608995731b32f
1 in β†’ 1 out7.8800 XPM109 B
AUMQRepm…tAfKmdW1
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.

1.875 Γ— 10⁹⁸(99-digit number)
18759883260646504255…10153303451423989760
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
1.875 Γ— 10⁹⁸(99-digit number)
18759883260646504255…10153303451423989759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.751 Γ— 10⁹⁸(99-digit number)
37519766521293008510…20306606902847979519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.503 Γ— 10⁹⁸(99-digit number)
75039533042586017021…40613213805695959039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.500 Γ— 10⁹⁹(100-digit number)
15007906608517203404…81226427611391918079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.001 Γ— 10⁹⁹(100-digit number)
30015813217034406808…62452855222783836159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.003 Γ— 10⁹⁹(100-digit number)
60031626434068813616…24905710445567672319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.200 Γ— 10¹⁰⁰(101-digit number)
12006325286813762723…49811420891135344639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.401 Γ— 10¹⁰⁰(101-digit number)
24012650573627525446…99622841782270689279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.802 Γ— 10¹⁰⁰(101-digit number)
48025301147255050893…99245683564541378559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.605 Γ— 10¹⁰⁰(101-digit number)
96050602294510101787…98491367129082757119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.921 Γ— 10¹⁰¹(102-digit number)
19210120458902020357…96982734258165514239
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 2991153

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 9d903018ab47e6e8cf833b3e74eed64f8424cf25f7e789ff7cdb3dd8dac8188c

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 #2,991,153 on Chainz β†—
Circulating Supply:57,970,374 XPMΒ·at block #6,840,753 Β· updates every 60s
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