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Block #370,205

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/21/2014, 10:30:58 PM Β· Difficulty 10.4469 Β· 6,457,006 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e2b2fd81218a3f6f5b57777c469edc577af9274a00f06e76aa1186130e050233
View on Chainz β†—

Height

#370,205

Difficulty

10.446922

Transactions

1

Size

210 B

Version

2

Bits

0a72697c

Nonce

6,051

Timestamp

1/21/2014, 10:30:58 PM

Confirmations

6,457,006

Merkle Root

b34fb1391855de58c8fa82c56e750bc391b4916f7d461276d02c59b4d08ac44c
Transactions (1)
Coinbaseb34fb1391855de…2c59b4d08ac44c
1 in β†’ 1 out9.1500 XPM116 B
AbwWkWZt…kawDhufa
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.

8.457 Γ— 10¹⁰³(104-digit number)
84571952197137067475…19847331100098560000
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
8.457 Γ— 10¹⁰³(104-digit number)
84571952197137067475…19847331100098559999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.457 Γ— 10¹⁰³(104-digit number)
84571952197137067475…19847331100098560001
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
1.691 Γ— 10¹⁰⁴(105-digit number)
16914390439427413495…39694662200197119999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.691 Γ— 10¹⁰⁴(105-digit number)
16914390439427413495…39694662200197120001
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
3.382 Γ— 10¹⁰⁴(105-digit number)
33828780878854826990…79389324400394239999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.382 Γ— 10¹⁰⁴(105-digit number)
33828780878854826990…79389324400394240001
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
6.765 Γ— 10¹⁰⁴(105-digit number)
67657561757709653980…58778648800788479999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.765 Γ— 10¹⁰⁴(105-digit number)
67657561757709653980…58778648800788480001
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
1.353 Γ— 10¹⁰⁡(106-digit number)
13531512351541930796…17557297601576959999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.353 Γ— 10¹⁰⁡(106-digit number)
13531512351541930796…17557297601576960001
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 370205

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 e2b2fd81218a3f6f5b57777c469edc577af9274a00f06e76aa1186130e050233

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 #370,205 on Chainz β†—
Circulating Supply:57,861,786 XPMΒ·at block #6,827,210 Β· updates every 60s
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