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Block #502,966

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/20/2014, 6:42:05 PM Β· Difficulty 10.8085 Β· 6,311,086 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
82029aad5c64de57e63b6b0eff37ebccc7c9bf46133319a40b9156fd65cf1faa
View on Chainz β†—

Height

#502,966

Difficulty

10.808451

Transactions

1

Size

202 B

Version

2

Bits

0acef6a0

Nonce

369,087,030

Timestamp

4/20/2014, 6:42:05 PM

Confirmations

6,311,086

Merkle Root

0f0ea53f0bf0b4d26a810aa3e71da20ef28dc0e02ffa94415b5e0e6d6107bf98
Transactions (1)
Coinbase0f0ea53f0bf0b4…5e0e6d6107bf98
1 in β†’ 1 out8.5500 XPM110 B
AJVvFGfN…wSDiQ8qP
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.

9.749 Γ— 10⁹⁹(100-digit number)
97495888731197546917…19810262264027934720
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
9.749 Γ— 10⁹⁹(100-digit number)
97495888731197546917…19810262264027934719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.749 Γ— 10⁹⁹(100-digit number)
97495888731197546917…19810262264027934721
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
1.949 Γ— 10¹⁰⁰(101-digit number)
19499177746239509383…39620524528055869439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.949 Γ— 10¹⁰⁰(101-digit number)
19499177746239509383…39620524528055869441
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
3.899 Γ— 10¹⁰⁰(101-digit number)
38998355492479018767…79241049056111738879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.899 Γ— 10¹⁰⁰(101-digit number)
38998355492479018767…79241049056111738881
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
7.799 Γ— 10¹⁰⁰(101-digit number)
77996710984958037534…58482098112223477759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.799 Γ— 10¹⁰⁰(101-digit number)
77996710984958037534…58482098112223477761
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
1.559 Γ— 10¹⁰¹(102-digit number)
15599342196991607506…16964196224446955519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.559 Γ— 10¹⁰¹(102-digit number)
15599342196991607506…16964196224446955521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.119 Γ— 10¹⁰¹(102-digit number)
31198684393983215013…33928392448893911039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 502966

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 82029aad5c64de57e63b6b0eff37ebccc7c9bf46133319a40b9156fd65cf1faa

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 #502,966 on Chainz β†—
Circulating Supply:57,756,492 XPMΒ·at block #6,814,051 Β· updates every 60s
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