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Block #276,803

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/27/2013, 8:08:37 AM Β· Difficulty 9.9643 Β· 6,518,262 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4ec176dc79f9549df89f7cc625db151c9634e7233ebcc6acd37302e7a094894b
View on Chainz β†—

Height

#276,803

Difficulty

9.964269

Transactions

1

Size

212 B

Version

2

Bits

09f6da55

Nonce

1,021

Timestamp

11/27/2013, 8:08:37 AM

Confirmations

6,518,262

Merkle Root

144ff4effd0931b71e015cd48b186c43196b8374f3baa561ac323b3fe5cb5ebe
Transactions (1)
Coinbase144ff4effd0931…323b3fe5cb5ebe
1 in β†’ 1 out10.0600 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.952 Γ— 10¹⁰⁸(109-digit number)
29520733854004068333…87747327455877529600
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
2.952 Γ— 10¹⁰⁸(109-digit number)
29520733854004068333…87747327455877529599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.952 Γ— 10¹⁰⁸(109-digit number)
29520733854004068333…87747327455877529601
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
5.904 Γ— 10¹⁰⁸(109-digit number)
59041467708008136666…75494654911755059199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.904 Γ— 10¹⁰⁸(109-digit number)
59041467708008136666…75494654911755059201
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
1.180 Γ— 10¹⁰⁹(110-digit number)
11808293541601627333…50989309823510118399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.180 Γ— 10¹⁰⁹(110-digit number)
11808293541601627333…50989309823510118401
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
2.361 Γ— 10¹⁰⁹(110-digit number)
23616587083203254666…01978619647020236799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.361 Γ— 10¹⁰⁹(110-digit number)
23616587083203254666…01978619647020236801
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
4.723 Γ— 10¹⁰⁹(110-digit number)
47233174166406509332…03957239294040473599
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 276803

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 4ec176dc79f9549df89f7cc625db151c9634e7233ebcc6acd37302e7a094894b

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 #276,803 on Chainz β†—
Circulating Supply:57,604,562 XPMΒ·at block #6,795,064 Β· updates every 60s
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