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Block #1,534,529

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 7:35:41 AM Β· Difficulty 10.6169 Β· 5,291,675 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
66dbc82c50a6ec76190ec40876b16b7475bf9497ef52dfd7109800de71e6bd4d
View on Chainz β†—

Difficulty

10.616862

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9deab1

Nonce

698,683,323

Timestamp

4/10/2016, 7:35:41 AM

Confirmations

5,291,675

Merkle Root

5a2ea63f22aaf6a27b7fac3c523bd1c44bce2a7b40e39c5c9423c2f72428b280
Transactions (2)
Coinbase9a8d28c563fba5…81ecb1560cec2d
1 in β†’ 1 out8.9400 XPM109 B
ALX3i9gR…aANqQpam
646bdd0469ea3d…ea4d8d6319bb96
51 in β†’ 1 out2817.7179 XPM7.41 KB
ATnFVTN6…1ZZ8VaoQ
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.

8.796 Γ— 10⁹⁡(96-digit number)
87969216672884691513…83847305147114534240
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
8.796 Γ— 10⁹⁡(96-digit number)
87969216672884691513…83847305147114534239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.796 Γ— 10⁹⁡(96-digit number)
87969216672884691513…83847305147114534241
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
1.759 Γ— 10⁹⁢(97-digit number)
17593843334576938302…67694610294229068479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.759 Γ— 10⁹⁢(97-digit number)
17593843334576938302…67694610294229068481
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
3.518 Γ— 10⁹⁢(97-digit number)
35187686669153876605…35389220588458136959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.518 Γ— 10⁹⁢(97-digit number)
35187686669153876605…35389220588458136961
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
7.037 Γ— 10⁹⁢(97-digit number)
70375373338307753210…70778441176916273919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.037 Γ— 10⁹⁢(97-digit number)
70375373338307753210…70778441176916273921
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
1.407 Γ— 10⁹⁷(98-digit number)
14075074667661550642…41556882353832547839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.407 Γ— 10⁹⁷(98-digit number)
14075074667661550642…41556882353832547841
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 1534529

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 66dbc82c50a6ec76190ec40876b16b7475bf9497ef52dfd7109800de71e6bd4d

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 #1,534,529 on Chainz β†—
Circulating Supply:57,853,762 XPMΒ·at block #6,826,203 Β· updates every 60s
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