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Block #521,072

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2014, 6:18:13 AM Β· Difficulty 10.8606 Β· 6,278,862 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b3c86c046a70daa3485ef3c9d412f8bdcf70771658e63e541b04207ca63f1553
View on Chainz β†—

Height

#521,072

Difficulty

10.860619

Transactions

1

Size

201 B

Version

2

Bits

0adc518f

Nonce

28,654

Timestamp

5/2/2014, 6:18:13 AM

Confirmations

6,278,862

Merkle Root

e56d0c6e9b69dc8594ca2504857f8fb1fb04e353ecc06bb074d5d6c921d92573
Transactions (1)
Coinbasee56d0c6e9b69dc…d5d6c921d92573
1 in β†’ 1 out8.4600 XPM110 B
AeKNrjNj…1NEq95Ta
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.

3.962 Γ— 10⁹⁷(98-digit number)
39629173671113924947…78211491626349780400
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
3.962 Γ— 10⁹⁷(98-digit number)
39629173671113924947…78211491626349780399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.962 Γ— 10⁹⁷(98-digit number)
39629173671113924947…78211491626349780401
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
7.925 Γ— 10⁹⁷(98-digit number)
79258347342227849894…56422983252699560799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.925 Γ— 10⁹⁷(98-digit number)
79258347342227849894…56422983252699560801
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
1.585 Γ— 10⁹⁸(99-digit number)
15851669468445569978…12845966505399121599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.585 Γ— 10⁹⁸(99-digit number)
15851669468445569978…12845966505399121601
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
3.170 Γ— 10⁹⁸(99-digit number)
31703338936891139957…25691933010798243199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.170 Γ— 10⁹⁸(99-digit number)
31703338936891139957…25691933010798243201
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
6.340 Γ— 10⁹⁸(99-digit number)
63406677873782279915…51383866021596486399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.340 Γ— 10⁹⁸(99-digit number)
63406677873782279915…51383866021596486401
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 521072

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 b3c86c046a70daa3485ef3c9d412f8bdcf70771658e63e541b04207ca63f1553

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 #521,072 on Chainz β†—
Circulating Supply:57,643,532 XPMΒ·at block #6,799,933 Β· updates every 60s
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