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Block #269,862

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/23/2013, 12:46:22 PM Β· Difficulty 9.9520 Β· 6,526,756 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a00d85420652fb9e82acbdb3592ce3c3d5f7cce57358e4b37a62dfbe7c6d3e2c
View on Chainz β†—

Height

#269,862

Difficulty

9.952015

Transactions

1

Size

206 B

Version

2

Bits

09f3b743

Nonce

50,332,298

Timestamp

11/23/2013, 12:46:22 PM

Confirmations

6,526,756

Merkle Root

0fd3e7d84446f831868fc8ea206ddb3322e40c0cf66e4738a0f1898eb0a5df04
Transactions (1)
Coinbase0fd3e7d84446f8…f1898eb0a5df04
1 in β†’ 1 out10.0800 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.

1.212 Γ— 10⁹⁡(96-digit number)
12127325327032028464…28791503940875781400
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
1.212 Γ— 10⁹⁡(96-digit number)
12127325327032028464…28791503940875781399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.212 Γ— 10⁹⁡(96-digit number)
12127325327032028464…28791503940875781401
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
2.425 Γ— 10⁹⁡(96-digit number)
24254650654064056928…57583007881751562799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.425 Γ— 10⁹⁡(96-digit number)
24254650654064056928…57583007881751562801
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
4.850 Γ— 10⁹⁡(96-digit number)
48509301308128113856…15166015763503125599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.850 Γ— 10⁹⁡(96-digit number)
48509301308128113856…15166015763503125601
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
9.701 Γ— 10⁹⁡(96-digit number)
97018602616256227712…30332031527006251199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.701 Γ— 10⁹⁡(96-digit number)
97018602616256227712…30332031527006251201
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
1.940 Γ— 10⁹⁢(97-digit number)
19403720523251245542…60664063054012502399
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 269862

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 a00d85420652fb9e82acbdb3592ce3c3d5f7cce57358e4b37a62dfbe7c6d3e2c

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 #269,862 on Chainz β†—
Circulating Supply:57,616,942 XPMΒ·at block #6,796,617 Β· updates every 60s
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