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Block #74,629

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 12:08:54 PM Β· Difficulty 8.9956 Β· 6,724,195 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cad9028dd40d2eb5cf4bbea9bd19172fe33dadade8a314248a92ea51cfbed7c1
View on Chainz β†—

Height

#74,629

Difficulty

8.995627

Transactions

1

Size

203 B

Version

2

Bits

08fee169

Nonce

145

Timestamp

7/21/2013, 12:08:54 PM

Confirmations

6,724,195

Merkle Root

c961e26ab7bbe5230ccd4d16d446044b0c6970d5b26bf73f68ef3bdb65b2c007
Transactions (1)
Coinbasec961e26ab7bbe5…ef3bdb65b2c007
1 in β†’ 1 out12.3400 XPM110 B
AFyH24t7…FypwiQVM
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.

1.679 Γ— 10¹⁰²(103-digit number)
16793515486146277112…34724294469775874080
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
1.679 Γ— 10¹⁰²(103-digit number)
16793515486146277112…34724294469775874079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.679 Γ— 10¹⁰²(103-digit number)
16793515486146277112…34724294469775874081
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
3.358 Γ— 10¹⁰²(103-digit number)
33587030972292554225…69448588939551748159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.358 Γ— 10¹⁰²(103-digit number)
33587030972292554225…69448588939551748161
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
6.717 Γ— 10¹⁰²(103-digit number)
67174061944585108451…38897177879103496319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.717 Γ— 10¹⁰²(103-digit number)
67174061944585108451…38897177879103496321
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
1.343 Γ— 10¹⁰³(104-digit number)
13434812388917021690…77794355758206992639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.343 Γ— 10¹⁰³(104-digit number)
13434812388917021690…77794355758206992641
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
2.686 Γ— 10¹⁰³(104-digit number)
26869624777834043380…55588711516413985279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9
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 74629

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 cad9028dd40d2eb5cf4bbea9bd19172fe33dadade8a314248a92ea51cfbed7c1

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 #74,629 on Chainz β†—
Circulating Supply:57,634,621 XPMΒ·at block #6,798,823 Β· updates every 60s
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