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Block #703,455

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2014, 2:08:22 AM Β· Difficulty 10.9590 Β· 6,108,286 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fd786f4bd6cc6e554813326a42d1b5c272bfd8ac046ad9463c052fa70815b083
View on Chainz β†—

Height

#703,455

Difficulty

10.958993

Transactions

2

Size

431 B

Version

2

Bits

0af58091

Nonce

106,702,294

Timestamp

9/2/2014, 2:08:22 AM

Confirmations

6,108,286

Merkle Root

69687f2d9359b3a90dfede8034a12a87ea47bde527daf8611bed5a2656981ff2
Transactions (2)
Coinbase0aeaf9bb3e9f19…68cd434e8b131d
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
01cd559f234c06…fab05cc90b1f34
1 in β†’ 2 out5.9733 XPM225 B
ATUJFkEF…j71DTZhmAKa7jb5A…AoWrwmKT
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.

1.233 Γ— 10⁹⁴(95-digit number)
12334400627578000289…09597255976215808980
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
1.233 Γ— 10⁹⁴(95-digit number)
12334400627578000289…09597255976215808979
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.233 Γ— 10⁹⁴(95-digit number)
12334400627578000289…09597255976215808981
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
2.466 Γ— 10⁹⁴(95-digit number)
24668801255156000579…19194511952431617959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.466 Γ— 10⁹⁴(95-digit number)
24668801255156000579…19194511952431617961
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
4.933 Γ— 10⁹⁴(95-digit number)
49337602510312001158…38389023904863235919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.933 Γ— 10⁹⁴(95-digit number)
49337602510312001158…38389023904863235921
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
9.867 Γ— 10⁹⁴(95-digit number)
98675205020624002317…76778047809726471839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.867 Γ— 10⁹⁴(95-digit number)
98675205020624002317…76778047809726471841
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
1.973 Γ— 10⁹⁡(96-digit number)
19735041004124800463…53556095619452943679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.973 Γ— 10⁹⁡(96-digit number)
19735041004124800463…53556095619452943681
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 703455

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 fd786f4bd6cc6e554813326a42d1b5c272bfd8ac046ad9463c052fa70815b083

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 #703,455 on Chainz β†—
Circulating Supply:57,738,037 XPMΒ·at block #6,811,740 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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