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Block #601,860

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/25/2014, 8:56:54 PM Β· Difficulty 10.9140 Β· 6,196,901 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
46ae3de743c6e297b7c8948d992ff65f5bda66cdc675b592067d6696ac44d3ec
View on Chainz β†—

Height

#601,860

Difficulty

10.913968

Transactions

1

Size

209 B

Version

2

Bits

0ae9f9d4

Nonce

1,023,656,852

Timestamp

6/25/2014, 8:56:54 PM

Confirmations

6,196,901

Merkle Root

d3a58996649a8d5999796edc2e791fbd4164c63549b960a0f981de452dadfbb6
Transactions (1)
Coinbased3a58996649a8d…81de452dadfbb6
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
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.

6.547 Γ— 10¹⁰¹(102-digit number)
65472349781093708824…39529610547703971840
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
6.547 Γ— 10¹⁰¹(102-digit number)
65472349781093708824…39529610547703971839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.547 Γ— 10¹⁰¹(102-digit number)
65472349781093708824…39529610547703971841
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
1.309 Γ— 10¹⁰²(103-digit number)
13094469956218741764…79059221095407943679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.309 Γ— 10¹⁰²(103-digit number)
13094469956218741764…79059221095407943681
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
2.618 Γ— 10¹⁰²(103-digit number)
26188939912437483529…58118442190815887359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.618 Γ— 10¹⁰²(103-digit number)
26188939912437483529…58118442190815887361
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
5.237 Γ— 10¹⁰²(103-digit number)
52377879824874967059…16236884381631774719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.237 Γ— 10¹⁰²(103-digit number)
52377879824874967059…16236884381631774721
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
1.047 Γ— 10¹⁰³(104-digit number)
10475575964974993411…32473768763263549439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.047 Γ— 10¹⁰³(104-digit number)
10475575964974993411…32473768763263549441
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
2.095 Γ— 10¹⁰³(104-digit number)
20951151929949986823…64947537526527098879
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 601860

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 46ae3de743c6e297b7c8948d992ff65f5bda66cdc675b592067d6696ac44d3ec

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 #601,860 on Chainz β†—
Circulating Supply:57,634,115 XPMΒ·at block #6,798,760 Β· updates every 60s
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