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Block #447,661

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/17/2014, 10:17:03 AM Β· Difficulty 10.3602 Β· 6,358,928 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b2677dac603e8cde533b1f183feb603d4e6e8d1d2bc390b17d988ba548ac911a
View on Chainz β†—

Height

#447,661

Difficulty

10.360223

Transactions

1

Size

203 B

Version

2

Bits

0a5c378e

Nonce

74,498

Timestamp

3/17/2014, 10:17:03 AM

Confirmations

6,358,928

Merkle Root

ef1131773ff74e26d918d2560a306d66d8dfde9838c9e2467c1161c800caeaa4
Transactions (1)
Coinbaseef1131773ff74e…1161c800caeaa4
1 in β†’ 1 out9.3000 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.

9.417 Γ— 10¹⁰¹(102-digit number)
94173133811577987951…08364499532326416640
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
9.417 Γ— 10¹⁰¹(102-digit number)
94173133811577987951…08364499532326416639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.417 Γ— 10¹⁰¹(102-digit number)
94173133811577987951…08364499532326416641
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
1.883 Γ— 10¹⁰²(103-digit number)
18834626762315597590…16728999064652833279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.883 Γ— 10¹⁰²(103-digit number)
18834626762315597590…16728999064652833281
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
3.766 Γ— 10¹⁰²(103-digit number)
37669253524631195180…33457998129305666559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.766 Γ— 10¹⁰²(103-digit number)
37669253524631195180…33457998129305666561
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
7.533 Γ— 10¹⁰²(103-digit number)
75338507049262390361…66915996258611333119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.533 Γ— 10¹⁰²(103-digit number)
75338507049262390361…66915996258611333121
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
1.506 Γ— 10¹⁰³(104-digit number)
15067701409852478072…33831992517222666239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.506 Γ— 10¹⁰³(104-digit number)
15067701409852478072…33831992517222666241
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 447661

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 b2677dac603e8cde533b1f183feb603d4e6e8d1d2bc390b17d988ba548ac911a

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 #447,661 on Chainz β†—
Circulating Supply:57,696,809 XPMΒ·at block #6,806,588 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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