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Block #310,031

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2013, 9:26:32 PM Β· Difficulty 9.9950 Β· 6,493,174 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
1c849b8c23142c701fb5669d3fcc620fd2a6d2780a27651c5eb1611a4b34060b
View on Chainz β†—

Height

#310,031

Difficulty

9.995035

Transactions

1

Size

1.11 KB

Version

2

Bits

09feba95

Nonce

34,029

Timestamp

12/13/2013, 9:26:32 PM

Confirmations

6,493,174

Merkle Root

0e77ca34378852b7f122dd1b50d74a2bd7b3023cd08b00b11a89c16e1fa01e70
Transactions (1)
Coinbase0e77ca34378852…89c16e1fa01e70
1 in β†’ 29 out9.9700 XPM1.02 KB
AJzWx2VD…j4ZSMit5Aac9Hjdg…P4ktypc3AZ2pPuKg…95SN2Yr7AUoys5KV…JenkuQ1FAQyr8Lw3…hs4nt3Pn
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.

5.717 Γ— 10⁹²(93-digit number)
57177584289290231181…47922588117618790400
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.717 Γ— 10⁹²(93-digit number)
57177584289290231181…47922588117618790399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.717 Γ— 10⁹²(93-digit number)
57177584289290231181…47922588117618790401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.143 Γ— 10⁹³(94-digit number)
11435516857858046236…95845176235237580799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.143 Γ— 10⁹³(94-digit number)
11435516857858046236…95845176235237580801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.287 Γ— 10⁹³(94-digit number)
22871033715716092472…91690352470475161599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.287 Γ— 10⁹³(94-digit number)
22871033715716092472…91690352470475161601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.574 Γ— 10⁹³(94-digit number)
45742067431432184945…83380704940950323199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.574 Γ— 10⁹³(94-digit number)
45742067431432184945…83380704940950323201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
9.148 Γ— 10⁹³(94-digit number)
91484134862864369890…66761409881900646399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.148 Γ— 10⁹³(94-digit number)
91484134862864369890…66761409881900646401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 310031

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 1c849b8c23142c701fb5669d3fcc620fd2a6d2780a27651c5eb1611a4b34060b

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 #310,031 on Chainz β†—
Circulating Supply:57,669,662 XPMΒ·at block #6,803,204 Β· updates every 60s
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