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Block #39,073

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 12:56:25 PM Β· Difficulty 8.2726 Β· 6,787,913 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c619326e7e577529b630c87517e5f4bab09fe350a5b97ccf26ec380a63a52b1b
View on Chainz β†—

Height

#39,073

Difficulty

8.272638

Transactions

1

Size

199 B

Version

2

Bits

0845cba0

Nonce

316

Timestamp

7/14/2013, 12:56:25 PM

Confirmations

6,787,913

Merkle Root

51bccded0500fbd8e526c45f1f841dd937f084768abc00da6498433439380253
Transactions (1)
Coinbase51bccded0500fb…98433439380253
1 in β†’ 1 out14.5900 XPM110 B
AWfebMWE…GqTaobyQ
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.

1.383 Γ— 10⁹³(94-digit number)
13836205505091041971…73381760893381024600
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
1.383 Γ— 10⁹³(94-digit number)
13836205505091041971…73381760893381024599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.383 Γ— 10⁹³(94-digit number)
13836205505091041971…73381760893381024601
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
2.767 Γ— 10⁹³(94-digit number)
27672411010182083943…46763521786762049199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.767 Γ— 10⁹³(94-digit number)
27672411010182083943…46763521786762049201
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
5.534 Γ— 10⁹³(94-digit number)
55344822020364167887…93527043573524098399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.534 Γ— 10⁹³(94-digit number)
55344822020364167887…93527043573524098401
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
1.106 Γ— 10⁹⁴(95-digit number)
11068964404072833577…87054087147048196799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.106 Γ— 10⁹⁴(95-digit number)
11068964404072833577…87054087147048196801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 39073

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 c619326e7e577529b630c87517e5f4bab09fe350a5b97ccf26ec380a63a52b1b

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 #39,073 on Chainz β†—
Circulating Supply:57,860,063 XPMΒ·at block #6,826,985 Β· updates every 60s
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