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Block #367,628

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/20/2014, 5:33:56 AM Β· Difficulty 10.4333 Β· 6,427,358 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3d61907d40f3c1209ec84d9f2627593f720c5c5c94880fd2147dcb7ee7a7a2a4
View on Chainz β†—

Height

#367,628

Difficulty

10.433316

Transactions

1

Size

210 B

Version

2

Bits

0a6eedce

Nonce

214,589

Timestamp

1/20/2014, 5:33:56 AM

Confirmations

6,427,358

Merkle Root

cca3d5e8e3e75d1ce1bea590d060ea224081e8ed0afed9cebc0e19e5426104ea
Transactions (1)
Coinbasecca3d5e8e3e75d…0e19e5426104ea
1 in β†’ 1 out9.1700 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.

3.518 Γ— 10¹⁰³(104-digit number)
35185925100577360857…49186560217174184640
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
3.518 Γ— 10¹⁰³(104-digit number)
35185925100577360857…49186560217174184639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.518 Γ— 10¹⁰³(104-digit number)
35185925100577360857…49186560217174184641
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
7.037 Γ— 10¹⁰³(104-digit number)
70371850201154721714…98373120434348369279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.037 Γ— 10¹⁰³(104-digit number)
70371850201154721714…98373120434348369281
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
1.407 Γ— 10¹⁰⁴(105-digit number)
14074370040230944342…96746240868696738559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.407 Γ— 10¹⁰⁴(105-digit number)
14074370040230944342…96746240868696738561
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
2.814 Γ— 10¹⁰⁴(105-digit number)
28148740080461888685…93492481737393477119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.814 Γ— 10¹⁰⁴(105-digit number)
28148740080461888685…93492481737393477121
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
5.629 Γ— 10¹⁰⁴(105-digit number)
56297480160923777371…86984963474786954239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.629 Γ— 10¹⁰⁴(105-digit number)
56297480160923777371…86984963474786954241
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 367628

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 3d61907d40f3c1209ec84d9f2627593f720c5c5c94880fd2147dcb7ee7a7a2a4

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 #367,628 on Chainz β†—
Circulating Supply:57,603,928 XPMΒ·at block #6,794,985 Β· updates every 60s
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