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Block #212,935

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 10/16/2013, 2:40:33 PM Β· Difficulty 9.9197 Β· 6,593,834 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f62cf4ea01fdc468f3c400cc16d2dc289ebcc1ef97fb37035dfd59cec100ce0d
View on Chainz β†—

Height

#212,935

Difficulty

9.919658

Transactions

1

Size

209 B

Version

2

Bits

09eb6eb5

Nonce

16,780,509

Timestamp

10/16/2013, 2:40:33 PM

Confirmations

6,593,834

Merkle Root

bf91c23651df3193aba9deafffcfae7ead2e6d52520bf753104418051b85213f
Transactions (1)
Coinbasebf91c23651df31…4418051b85213f
1 in β†’ 1 out10.1500 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.823 Γ— 10¹⁰²(103-digit number)
28236400479629987953…48846045270744128000
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
2.823 Γ— 10¹⁰²(103-digit number)
28236400479629987953…48846045270744127999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.823 Γ— 10¹⁰²(103-digit number)
28236400479629987953…48846045270744128001
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
5.647 Γ— 10¹⁰²(103-digit number)
56472800959259975907…97692090541488255999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.647 Γ— 10¹⁰²(103-digit number)
56472800959259975907…97692090541488256001
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
1.129 Γ— 10¹⁰³(104-digit number)
11294560191851995181…95384181082976511999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.129 Γ— 10¹⁰³(104-digit number)
11294560191851995181…95384181082976512001
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
2.258 Γ— 10¹⁰³(104-digit number)
22589120383703990363…90768362165953023999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.258 Γ— 10¹⁰³(104-digit number)
22589120383703990363…90768362165953024001
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
4.517 Γ— 10¹⁰³(104-digit number)
45178240767407980726…81536724331906047999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.517 Γ— 10¹⁰³(104-digit number)
45178240767407980726…81536724331906048001
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
9.035 Γ— 10¹⁰³(104-digit number)
90356481534815961452…63073448663812095999
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
9.035 Γ— 10¹⁰³(104-digit number)
90356481534815961452…63073448663812096001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 212935

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 f62cf4ea01fdc468f3c400cc16d2dc289ebcc1ef97fb37035dfd59cec100ce0d

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 #212,935 on Chainz β†—
Circulating Supply:57,698,254 XPMΒ·at block #6,806,768 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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