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Block #460,554

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/26/2014, 2:38:22 AM Β· Difficulty 10.4167 Β· 6,354,324 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a3a4e31937b70ef411c882fcc187d34c8a11bc507a45df6f11a1cb9f761e73b1
View on Chainz β†—

Height

#460,554

Difficulty

10.416667

Transactions

1

Size

203 B

Version

2

Bits

0a6aaaae

Nonce

235,429

Timestamp

3/26/2014, 2:38:22 AM

Confirmations

6,354,324

Merkle Root

e9ada6464b3c7514ae7dd0ab442a460af80df7f8bab9bfa78303ea519c0d71ca
Transactions (1)
Coinbasee9ada6464b3c75…03ea519c0d71ca
1 in β†’ 1 out9.2000 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.

1.042 Γ— 10¹⁰²(103-digit number)
10425809714676553295…37706217612503151520
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
1.042 Γ— 10¹⁰²(103-digit number)
10425809714676553295…37706217612503151519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.042 Γ— 10¹⁰²(103-digit number)
10425809714676553295…37706217612503151521
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
2.085 Γ— 10¹⁰²(103-digit number)
20851619429353106590…75412435225006303039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.085 Γ— 10¹⁰²(103-digit number)
20851619429353106590…75412435225006303041
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
4.170 Γ— 10¹⁰²(103-digit number)
41703238858706213180…50824870450012606079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.170 Γ— 10¹⁰²(103-digit number)
41703238858706213180…50824870450012606081
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
8.340 Γ— 10¹⁰²(103-digit number)
83406477717412426360…01649740900025212159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.340 Γ— 10¹⁰²(103-digit number)
83406477717412426360…01649740900025212161
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
1.668 Γ— 10¹⁰³(104-digit number)
16681295543482485272…03299481800050424319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.668 Γ— 10¹⁰³(104-digit number)
16681295543482485272…03299481800050424321
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 460554

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 a3a4e31937b70ef411c882fcc187d34c8a11bc507a45df6f11a1cb9f761e73b1

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 #460,554 on Chainz β†—
Circulating Supply:57,763,111 XPMΒ·at block #6,814,877 Β· updates every 60s
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