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Block #142,469

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/30/2013, 11:46:33 PM Β· Difficulty 9.8373 Β· 6,657,471 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b20d3b281408b91f5fbc10212f097fe3217bde2ae54bf016d7e7d57879326e15
View on Chainz β†—

Height

#142,469

Difficulty

9.837270

Transactions

1

Size

200 B

Version

2

Bits

09d6575c

Nonce

350,400

Timestamp

8/30/2013, 11:46:33 PM

Confirmations

6,657,471

Merkle Root

2c4a8c55fb1964d8eb2317af8eef14815ef7275bdb923c74200ae4f6abe87743
Transactions (1)
Coinbase2c4a8c55fb1964…0ae4f6abe87743
1 in β†’ 1 out10.3200 XPM109 B
AZxVto6u…BDiviSjb
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.

3.306 Γ— 10⁹⁢(97-digit number)
33061983986045317485…39765957561494162500
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
3.306 Γ— 10⁹⁢(97-digit number)
33061983986045317485…39765957561494162499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.612 Γ— 10⁹⁢(97-digit number)
66123967972090634970…79531915122988324999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.322 Γ— 10⁹⁷(98-digit number)
13224793594418126994…59063830245976649999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.644 Γ— 10⁹⁷(98-digit number)
26449587188836253988…18127660491953299999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.289 Γ— 10⁹⁷(98-digit number)
52899174377672507976…36255320983906599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.057 Γ— 10⁹⁸(99-digit number)
10579834875534501595…72510641967813199999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.115 Γ— 10⁹⁸(99-digit number)
21159669751069003190…45021283935626399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.231 Γ— 10⁹⁸(99-digit number)
42319339502138006381…90042567871252799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.463 Γ— 10⁹⁸(99-digit number)
84638679004276012762…80085135742505599999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 142469

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 b20d3b281408b91f5fbc10212f097fe3217bde2ae54bf016d7e7d57879326e15

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 #142,469 on Chainz β†—
Circulating Supply:57,643,581 XPMΒ·at block #6,799,939 Β· updates every 60s
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