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Block #61,090

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2013, 11:31:48 AM Β· Difficulty 8.9718 Β· 6,740,462 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
326af8168624f148ea25b290851b5730ebfab1c3042e9796505b45cbf8a5ce9a
View on Chainz β†—

Height

#61,090

Difficulty

8.971799

Transactions

1

Size

197 B

Version

2

Bits

08f8c7cf

Nonce

1,089

Timestamp

7/18/2013, 11:31:48 AM

Confirmations

6,740,462

Merkle Root

cc215b7928c1426e65929652134ab241c63d0da0614f357b09016756934fb7f1
Transactions (1)
Coinbasecc215b7928c142…016756934fb7f1
1 in β†’ 1 out12.4100 XPM110 B
AZhKuBRu…daViXERd
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.

2.162 Γ— 10⁸⁷(88-digit number)
21626346608127362480…98285592877370449460
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
2.162 Γ— 10⁸⁷(88-digit number)
21626346608127362480…98285592877370449459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.325 Γ— 10⁸⁷(88-digit number)
43252693216254724960…96571185754740898919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.650 Γ— 10⁸⁷(88-digit number)
86505386432509449920…93142371509481797839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.730 Γ— 10⁸⁸(89-digit number)
17301077286501889984…86284743018963595679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.460 Γ— 10⁸⁸(89-digit number)
34602154573003779968…72569486037927191359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.920 Γ— 10⁸⁸(89-digit number)
69204309146007559936…45138972075854382719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.384 Γ— 10⁸⁹(90-digit number)
13840861829201511987…90277944151708765439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.768 Γ— 10⁸⁹(90-digit number)
27681723658403023974…80555888303417530879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.536 Γ— 10⁸⁹(90-digit number)
55363447316806047948…61111776606835061759
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 61090

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 326af8168624f148ea25b290851b5730ebfab1c3042e9796505b45cbf8a5ce9a

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 #61,090 on Chainz β†—
Circulating Supply:57,656,495 XPMΒ·at block #6,801,551 Β· updates every 60s
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