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Block #478,761

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/7/2014, 7:02:34 AM Β· Difficulty 10.4962 Β· 6,333,649 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
01883105862c1acea09b080d7e93b7732cfdd5595773876eab4c55470587c7b4
View on Chainz β†—

Height

#478,761

Difficulty

10.496213

Transactions

1

Size

198 B

Version

2

Bits

0a7f07ca

Nonce

1,810,105,250

Timestamp

4/7/2014, 7:02:34 AM

Confirmations

6,333,649

Merkle Root

952097645848ce13be32d1f924aec5de9f79b6c256b19a441978b3152268f6c1
Transactions (1)
Coinbase952097645848ce…78b3152268f6c1
1 in β†’ 1 out9.0600 XPM109 B
ANqvhwKM…ivCXYXen
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.

3.282 Γ— 10⁹³(94-digit number)
32829606839847605467…68722723664819684230
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
3.282 Γ— 10⁹³(94-digit number)
32829606839847605467…68722723664819684229
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.282 Γ— 10⁹³(94-digit number)
32829606839847605467…68722723664819684231
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
6.565 Γ— 10⁹³(94-digit number)
65659213679695210935…37445447329639368459
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.565 Γ— 10⁹³(94-digit number)
65659213679695210935…37445447329639368461
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
1.313 Γ— 10⁹⁴(95-digit number)
13131842735939042187…74890894659278736919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.313 Γ— 10⁹⁴(95-digit number)
13131842735939042187…74890894659278736921
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
2.626 Γ— 10⁹⁴(95-digit number)
26263685471878084374…49781789318557473839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.626 Γ— 10⁹⁴(95-digit number)
26263685471878084374…49781789318557473841
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
5.252 Γ— 10⁹⁴(95-digit number)
52527370943756168748…99563578637114947679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.252 Γ— 10⁹⁴(95-digit number)
52527370943756168748…99563578637114947681
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 478761

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 01883105862c1acea09b080d7e93b7732cfdd5595773876eab4c55470587c7b4

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 #478,761 on Chainz β†—
Circulating Supply:57,743,307 XPMΒ·at block #6,812,409 Β· updates every 60s
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