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Block #1,231,521

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/11/2015, 8:48:40 AM Β· Difficulty 10.7387 Β· 5,595,202 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b5da4f3cdba4ae66cdcb7c30c8029566c9b287e65b49f25c383cd913e06a4518
View on Chainz β†—

Difficulty

10.738674

Transactions

1

Size

243 B

Version

2

Bits

0abd19c2

Nonce

8,082,370

Timestamp

9/11/2015, 8:48:40 AM

Confirmations

5,595,202

Merkle Root

673a851ba7779d886c7545b85c69c4fc213c0e86de50ac40374502d49270b94e
Transactions (1)
Coinbase673a851ba7779d…4502d49270b94e
1 in β†’ 2 out8.6600 XPM152 B
AMxYdoJ9…UHaf4EvRALPu3s2c…EJXLjVFh
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.

7.818 Γ— 10⁹⁷(98-digit number)
78189772836406334206…60452001840926003200
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
7.818 Γ— 10⁹⁷(98-digit number)
78189772836406334206…60452001840926003201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.563 Γ— 10⁹⁸(99-digit number)
15637954567281266841…20904003681852006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.127 Γ— 10⁹⁸(99-digit number)
31275909134562533682…41808007363704012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.255 Γ— 10⁹⁸(99-digit number)
62551818269125067365…83616014727408025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.251 Γ— 10⁹⁹(100-digit number)
12510363653825013473…67232029454816051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.502 Γ— 10⁹⁹(100-digit number)
25020727307650026946…34464058909632102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.004 Γ— 10⁹⁹(100-digit number)
50041454615300053892…68928117819264204801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.000 Γ— 10¹⁰⁰(101-digit number)
10008290923060010778…37856235638528409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.001 Γ— 10¹⁰⁰(101-digit number)
20016581846120021556…75712471277056819201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.003 Γ— 10¹⁰⁰(101-digit number)
40033163692240043113…51424942554113638401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1231521

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 b5da4f3cdba4ae66cdcb7c30c8029566c9b287e65b49f25c383cd913e06a4518

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 #1,231,521 on Chainz β†—
Circulating Supply:57,857,938 XPMΒ·at block #6,826,722 Β· updates every 60s
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