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Block #35,078

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 7:30:10 AM Β· Difficulty 7.9940 Β· 6,791,908 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b9e2218e18bb509bd223534f7d46c2278e807dfdb12778fafb2728640806efd4
View on Chainz β†—

Height

#35,078

Difficulty

7.994033

Transactions

1

Size

197 B

Version

2

Bits

07fe78f2

Nonce

361

Timestamp

7/14/2013, 7:30:10 AM

Confirmations

6,791,908

Merkle Root

e8d6e23890ad90b576fbff3d707e4ae44c5f4ec27092e5381c13f4b6505e7ec9
Transactions (1)
Coinbasee8d6e23890ad90…13f4b6505e7ec9
1 in β†’ 1 out15.6300 XPM109 B
AMAsrnsz…99mSq6AM
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.

2.516 Γ— 10⁹⁰(91-digit number)
25167901737732548638…13321487449335857680
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
2.516 Γ— 10⁹⁰(91-digit number)
25167901737732548638…13321487449335857679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.516 Γ— 10⁹⁰(91-digit number)
25167901737732548638…13321487449335857681
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
5.033 Γ— 10⁹⁰(91-digit number)
50335803475465097276…26642974898671715359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.033 Γ— 10⁹⁰(91-digit number)
50335803475465097276…26642974898671715361
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
1.006 Γ— 10⁹¹(92-digit number)
10067160695093019455…53285949797343430719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.006 Γ— 10⁹¹(92-digit number)
10067160695093019455…53285949797343430721
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
2.013 Γ— 10⁹¹(92-digit number)
20134321390186038910…06571899594686861439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7
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 35078

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 b9e2218e18bb509bd223534f7d46c2278e807dfdb12778fafb2728640806efd4

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 #35,078 on Chainz β†—
Circulating Supply:57,860,063 XPMΒ·at block #6,826,985 Β· updates every 60s
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